Affects of Lens Quality on Image Resolution DRAFT Version 3a July Tim Vitale 2011 use with permission only 1 - Introduction

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1 Affects of Lens Quality on Image Resolution DRAFT Version 3a July Tim Vitale 2011 use with permission only 1 - Introduction 1 Figure 1a - d: Uses and Faults of the Simple Lens 1 Figure 2a - d: Comparison of cellphone camera & dslr in cross-section 2 Figure 3a - b: Two components used in the Resolving Power Equation (1) sensor & (2) lens Lens History 3 Figure 4: Single-Element Lens Shapes 3 Figure 5: Diagram of 2-element Chevalier Lens (1839) 4 Figure 6: Diagram of 4-element Petzval Portrait Lens (1841) 4 Figure 7: Diagram of 3-element Cooke or Taylor Triplet Lens (1893) 4 Modern Lens Technology 5 Figure 8: Cross-section of Schneider Super-8 Film Variogon 6-180mm zoom lens (1970) 5 Table 1: Lens Resolution Estimator By Date and Format size Lens Issues Effecting Resolution 7 Figure 9a & b: Effect of f/stop Diameter on Relative Use of Glass in Lens 7 Figure 10: Iris Scattering Effect RPE for Evaluating image resolution in an Imaging System: Camera, Lens and Film/CCD/CMOS 8 Table 2: Selected Film and Lens Resolution Data 8 Table 3: Image Resolution for Three Film Shot thru Lenses of Increasing Resolving Power Lens Limits the Resolution of all Imaging Systems (film, digital or the future) 10 Figure 11: Effect of Lens Quality in Image Resolution 10 Performance of Prime vs Zoom Lens 10 Figure 12a, b & c: Photodo MTF data on Canon 50/1.4 & Canon 85/1.2 & Sigma zoom 11 Figure 13a & b: Contrast between black & white line-pairs and USAF 1951 target 12 Figure 14a & b: Two Slant Line test charts 12 The Influence of Lens Quality on Image Resolution 12 Figure 15: Film resolution degraded by the lens 13 Using an Average Lens (60-lp/mm) vs and Excellent Lens (100-lp/mm) 13 Figure 16: Lens MTF plots: Canon 35-mm format lenses 14 Figure 17: Lens MTF plots: Nikon 35-mm format lenses 15 Figure 18: Lens MTF plots: Leica 35-mm format lenses 16 6 Summary and Recommendations 16 Appendix 1 - Note on Digital Cameras 16 Appendix 2 List of Imaging Events Relevant to Lens History Introduction A camera s lens limits the resolution of the image produced by the camera s sensor. The lens is so important that even a quality lens will diminish image resolution by about half. Using a well-known equation for predicting image resolution it will be shown that an image made from a common slide film (Fuji Velvia) shot through a good quality lens will have about half the native resolution of the film. Changing film type (and thus resolution) and lens quality will influence image resolution, but the lens will always decrease the final resolution of the image. The lenses used in many compact digital cameras and cellphone cameras often suffer from chromatic and spherical aberrations, among the worst faults a lens can suffer. Figure 1 shows examples of these faults using images made from a single-element meniscus lens, such as was used in the 1956 Brownie Hawkeye. Note the non-straight lines in Figure 1d and color halos in Fig 1e. Figure 1a - 1d - Uses and Faults of the Simple Lens: Fig 1a, used in the Kodak s Brownie Hawkeye (1950s); Fig 1b, a diagram of the simple meniscus lens; Fig 1c, image of a meniscus lens with a fixed diaphragm; Fig 1d, an image shot through the lens showing spherical aberration (pincushion type fault); Fig 1e, is also an image shot through a meniscus lens showing chromatic aberrations where different colors of light focus in a different place based on wavelength size, notice the blue halo at the top of the word custom and the yellow at the bottom. Some of the images above were pulled from the blogger Silverbase s entry on astigmatism Modern dslr cameras can have excellent lenses when manufactured by one of the first-tier lens makers. The SLR camera was designed in the 1930s to take interchangeable lenses. The fixed focal length lenses from the era had are now called prime lenses, following the cinematographic lexicon. Zoom lenses came much later, and are now used almost universally. Prime lenses are capable of resolution equal to the best color film of the late 1990s (80 lp/mm or 4064 ppi digital equivalent) up to 120 lp/mm (6096 ppi digital equivalent) or the digital equivalent of a 24 MP dslr. The prime lenses with focal lengths in bold typeface below have the highest resolution possible

2 p 2 when they are made by first-tier manufacturers [Canon, Leica, Nikon and Zeiss]. The best of the lot, on a 24 MP body, will deliver the best possible image files. The images will be far better than film. Prime lens fall into groups based on their use, the current groups are defined as: Wide angle 14, 18, 20, 24, 28 and 35 mm Standard 50 mm Macro - 55, 65 and 105 Telephoto 85, 105, 135 and 200 mm Long telephoto 300, 400, 600, 800 and 1000 mm Zoom lenses are ubiquitous on dslrs today because their auto focus and auto zoom features make picture taking easy and extremely quick. They have their drawbacks because their designers have many more, competing, optical compromises to solve than a fixed focal length prime lens. Based on MTF-data found on the photodo.com website, zoom lenses have a minimum of 15-25% less resolution than the primes they replace, with as much as 60-75% less resolution for the worst of the group. No matter the quality of lens, zooms fall short of the capabilities of single focal length (prime) lenses, which are designed to solve all the competing optical properties for one focal length. Figure 2 shows cross-sections through both a Nikon D3 dslr and a cellphone camera (1 mm cube). The difference in scale shows two very different technologies. The full-sized image sensor in the dslr is roughly 24 x 36 mm, while the chip(s) in the cellphone cameras are roughly 3 x 5 mm (about 60x smaller). The pixel size on the small chips (Fig 2a) is about one micron (1-um) compared to the 8-um pixels in the full-sized Nikon D3 chip shown in Figure 2d. Small pixels are very noisy and thus allow a diminished range of usable exposures. Small chips, however, use small lens elements that are easier to design and manufacture. Small format lenses can have high resolution if made by first-tier manufacturers. However, price point is often a critical issue in small camera systems; manufacturers tend to use simple, less expensive, lenses. Some of the oldest lens designs (Figures 5, 6 & 7) are being used in those inexpensive compact cameras. The expensive ILC (Interchangeable Lens Compacts) cameras, such as the [Panasonic] Lumix GF1 ($900) and GS1 use the superior Leica DX zoom lens (4/3 rds chips, 13 x 18 mm, with 5-um pixels). Figure 2a - d: Comparison of cellphone cameras, with an auxiliary lens and a Nikon dslr in cross-section - Fig 2a, (upper left) shows a Sony 12 and 8 MP cellphone camera as standalone components, they are roughly 1-mm cubes. Fig 2b, (upper right) shows a similar cellphone camera with an auxiliary lens. Fig 2c, (lower left) is a cross-section of a cellphone camera with an auxiliary lens; note the 2-element lens in the heart of the cellphone camera (auxiliary lens is the large 5-element attachment). Fig 2d, (lower right) is a Nikon D3 dslr (12.1 MP with full sized sensor) in cross-section; note 12-element zoom lens.

3 p 3 The resolution of an imaging system is calculated using the Resolving Power Equation (RPE), which is explained and data tables are given in Section 4. The resolution of images has two main influences: the film (or media) and the lens. Thus, the RPE [equation] needs only two pieces of data: resolution of the media (film or digital) resolution of the lens Figure 3a & 3b - Two components used in the Resolving Power Equation (1) sensor and (2) lens - Fig 1a, the Sony 24.7 MP CMOS sensor (4032 x 6048 active, 5.9 um, pixels) with a sensor size of 32 x 41 mm (slightly larger than full size) that is being used in the Sony Alpha 850 and A 900 dslrs. Fig 1b, shows the cross-section of Nikon mm zoom lens which get a 4.0 Rating by photodo.com (MTF data) it probably can deliver 80- to 100-lp/mm at f/8 (about as good as a zoom lens can perform). Note on Digital Cameras: It is the nature of digital sensors that double the pixel content is necessary to be equivalent to the analog domain (film). The concept is explained by the Nyquist Sampling Theorem, which says that at least twice the digital bandwidth is required to capture analog information in the digital domain. A 24 MP camera has an equivalent number of pixels to the native resolution of common slide film (Fuji Velvia 4000x 6000). However, a 24 MP sensor only has the usable resolution equivalent to that slide film shot through a good quality lens -- about 2000 ppi, half the sensor s resolution. See Appendix 1 for details. 2 - Lens History Lenses have evolved from clear polished stones (5000 BP) to shaped ground-and-polished single glass lenses about 2800 BP. Both were used for close work such as examining fine detail and writing. Around 1000 AD the reading glass (magnifying glass) was developed in the west. During the 1300s eyeglass were shown in paintings. Beginning around 1608 the telescope was invented. It used two, single, ground and polished lenses at either end of a tube. Opticians were on the cutting edge of society. They developed lenses for reading (older eyes), common vision problems, military telescopes and systems for viewing the stars; see for details. Very early lenses tend to be made using one or two elements. Figure 4: Single-Element Lens Shapes - Examples of single lens elements. Most early lenses were built using these basic shapes. Note that the meniscus shape is forth from left. The image was pulled and simplified from livephysics.com/tools/optics/focal-length-forthin-lens.html The single-element lens design can be traced back to Egyptian hieroglyphics (2800 BP). A single lens can be used to focus light, but there are major optical faults such as spherical and chromatic aberration. A single lens cannot focus all colors of light in the same place. The meniscus lens (forth on right) was famously used in many of the Eastman Kodak series of brownie cameras beginning in 1908 through the 1960s; see nie-camera.com/. Figure 4 shows the six basic lens shapes. An early (1750) example of a 2-element design is the Hall Achromat, which used two glass types (crown and flint) to focus red and blue light in the same place, the focal point for green light was shifted, thus the design s resolution was soft and focused in a curved field, such as the back of the eye. The 1812 Wollaston Landscape lens (curved-field) was the first properly designed lens, but it also suffered from chromatic aberrations (focusing different colors in different planes). It is still used in use in low-cost applications such a compact and cellphone cameras.

4 p 4 The noted Chevalier Achromatic lens (1835) used two cemented glass elements (no air interface) made with different glass formulations; which corrected for two colors (Achromat) of light and focused in a flat field; see Figure 5. Curved filed lenses were quite workable in eyeglasses and telescopes, where the image is focused on the back of the eye, which has a curved field. Daguerre officially adopted the Chevalier lens in The design is still being used today in many point-and-shoot and cellphone cameras because it can be made easily using optical plastics and improved with multiple optical coatings. Photography spurred the development of lenses. About 1812, Niépce, the inventor of photography, was experimenting with silver-based images, but his images weren t permanent because John Herschel had not yet discovered a workable fixing agent (Hypo). Fixer removes the unexposed silver after the exposed silver has been developed into an image. Removing the unexposed silver prevents the image from darkening when exposed to room light. Photography was invented in 1826 when Niépce created an image using bitumen on polished Pewter metal. Figure 5: Diagram of earliest Chevalier Lens (1835) often called the French Landscape lens, image taken from Kingslake s: A History of the Photographic Lens (1989). This date is sometimes not accepted by historians because it was not silver chemistry, but rather the chemistry of an organic compound -- tar. Most Photography Curators accept 1839 as the date photography was invented because William Fox Talbot published on Photogenic Drawings and Louis Daguerre published on Daguerreotypes, both permanent silver images. In this era, average lenses probably delivered resolution of about lp/mm. Kingslake (noted lens historian) said it is hard to understand why the development of a good camera lens was such a slow process between 1840 and The explanation offered was that early opticians were using single lens elements (see Figure 4) as building blocks while seeking a happy accident. On the other hand, lens designers such as Petzval develop lenses on paper, using optical formulae (math) and then built them from the glass upwards. By 1841, Petzval designed the 4-element achromatic portrait lens, which became a photographic standard used through middle of the 20th century. It is thought to be capable of lp/mm, corrected for two colors with a flat field. It had a long shape due to a large air gap, and thus couldn t be Figure 6: Diagram of the Petzval 4- element portrait lens (1841). Different colors for elements denote different glass formulations. used in amateur cameras that favored the compact Chevalier and Dagor designs. The Petzval lens used different glass formulations to improve light handling, but still only corrected for two colors, not three. The famous German lens design atelier, Carl Zeiss AG, opened in 1846 in Jana (became East Germany after WWII), where they specialized in making lenses for microscopes. Zeiss collected the leading minds on glass formulation (Schott) and optical design (Abbe and Rudolph) to produce remarkable optics for all types of imaging systems of the era. The history of Carl Zeiss can be found at org/wiki/carl_zeiss_ag and zeiss.de/c12567 A100537AB9/Inhalt-Frame/819F178EC84030AC41256A F7C. Otto Schott joined Ernst Abbe and Carl Zeiss ss.htm to produce glass capable of implementing the workshop s first apochromatic lens flat field designs that corrected both spherical (3 colors) and chromatic aberrations (2 colors) in This development pushed possible lens resolutions up to of lp/mm. By 1896, the Zeiss workshop developed the Protar and Planar lens designs, which were significant developments. However, they only came into wide use after lens coating was developed 40 years later. A compact, 3-element, Dagor Anastigmatic flat field lens was produced by Goerz (Berlin) in 1904 and it is still being used today The design was a significant advance, correcting spherical aberration, coma and astigmatism, it s thought to be capable of lp/mm. Another famous lens that is still in common use, because of its compact design, is the Cooke or Taylor Triplet. In 1893, H. Dennis Taylor (optician) working for the famous Cooke company, used 3-elements as shown in Figure 7. The lens corrected all the classical aberrations to a high degree, Figure 7: Cooke or Taylor Triplet, 1893, used 3-elements to make many optical corrections, still used today because it compact and good enough for small digital chips.

5 p 5 including astigmatism (focusing at a point source) which enhanced image resolution markedly. This lens spawned numerous designs such as the Argus Cintar, Carl Zeiss Novar, Yashica Yashikor and Schneider Radionar. Most lens designs were developed by 1900 in the Zeiss workshop. At the turn-of-the-century, the next significant advancement in lens development was the 4-element 3-group Tessar design, which created higher contrast and thus greater resolution beginning in 1902; resolutions of lp/mm are possible. By 1935, Zeiss had also pioneered optical coatings for lenses surface. The coatings were used to cut down the scatter of light at the glass-air interfaces. This is important for the more complex designs (using 5- to 12-elements) that are more successful at resolving optical aberrations. Controlling light scatter was important because there was a 5% loss of light (from scatter) at each uncoated interface. A maximum of 10 air-glass interfaces are possible in a 5-element lens. Coatings were initially applied to military and 35-mm format lenses. The German designers continued to refine lens glass formulations and to introduce advanced coatings through WWII, this raised lens quality to a very high level. While the Allies did not share in these developments, the Hasselblad (Swedish) HK7 (1941) reconnaissance camera, used by the Allies about-hasselblad/history/a-man-with-small-hands.aspx, was said to be better than the captured German equivalent. Film and lenses were strategic war materials facilitating reconnaissance and espionage. These advancements did not reach the public until after the war. Lens coatings were not fully implemented in photographic lenses until about 1980, when the large-format lens makers such as Schneider, Rodenstock, Nikon, Fujinon and Caltar applied multiple coatings to every lens in their line. Multiple coatings can reduce light scattered from 5% to 0.5% (a 10x reduction) at each airglass interface, after the multi-coat technology was developed in the 1960s; see /wiki/antireflective_coating. Many older adults can remember using 2-¼ x 2-¼ (220-roll film) in a black box camera or one of the many configurations of the Kodak Brownie in the 1920s thru 1950s. Most of these cameras used the Chevalier 2- element Achromat type lens. By the 1960s, the baby boomers were smitten with the 35-mm format SLR (single lens reflex) camera with interchangeable wide-angle, standard and telephoto [prime] lenses. This began after 1950, when Nikkor lens quality (Nikon founded 1917) was found to be equal to Zeiss and Leica examples. The Japanese analogue of earlier German 35-mm rangefinders and SLRs cameras and lenses, along with the Army PX in the Vietnam Era, flooded the country with high quality optics and cameras. Figure 8: A Schneider image of an early Super-8 mm film Variogon F/1.8, 6-180mm zoom lens, with a huge number of lens elements (30+) and a spectacular 30x-zoom. It was made in 1970, for the Beaulieu (brand name) newsgathering motion picture cameras, which used narrow gauge (super-8 mm) film, rather than the more common 16 mm film. Zoom lenses were first used on TV and motion picture cameras in that era. Zoom lenses are in wide use today, however they have a minimum of 15-25%-less resolution than prime lenses. Further, zoom lenses can have 50% to 75% less resolution when used at their extremes and wide open. All lenses exhibit their best performance when stopped down 2-3 stops below wide open (smallest f- number). An overview of zoom lenses can be found at A year-by-year history of lenses can be found in the Appendix, where information on the development of photography and cameras is included to provide historical context. Lenses reached a penultimate state just before WWII, and topped out in the 1970s. Modern lenses (post- 1950) show small incremental improvements such as (i) multiple vacuum deposited coatings; (ii) nonyellowing element-to-element cement, (iii) exotic lens element shapes and (iv) exotic glass formulations to (a) reduce flare, (b) limit inter-element light scattering while (c) increasing sharpness and (d) increase contrast out to the edge of a (e) flat field. In general, the street value of a lens [within its format] is a rough indicator of its quality. The cost of specific lenses within a sub-group, such as the 35mm, 50mm or 85mm primes, or the ubiquitous 18/35mm to 70/85mm zoom, are examples. The best small format prime lenses perform at lp/mm; see Figures Medium and large format lenses sell in much small quantities, thus they are more expensive than 35-mm format lenses, while they have inherently less resolution. Modern Lens Technology Even today, lenses are the limiting factor in image quality. Most experienced photographers assume a 50% loss of media resolution (film, CD or CMOS) when using even the best lenses. The history of lens resolution can be roughly defined by the camera formats outlined below. Both the factors of (i) lens size and (ii) lens development thru photographic history are combined in Table 1, which estimates lens resolution through time.

6 p 6 Small format (35-mm format & dslrs) cameras will tend to have better lens quality ( lp/mm) than larger formats. Generally, this is because the lens elements are smaller and simpler to engineer and manufacture. However, most modern dslrs are sold with low-cost kit zoom lenses to keep the system cost low. Zoom lenses have lower resolution by their very nature, but kit lenses tend to be lower-cost versions of lenses with inherently less resolution. Prime lenses have the best resolution for the price; and the 35mm, 50mm, 85mm and 200mm primes tend to be the best performers within their full range. Wideangle primes (28 mm and less) are only capable of about 60-lp/mm. Professional photographers will tend to use better quality lenses while non-professionals often used kit or second-tier lenses. Medium format (MF) photographers tend to use high quality first-tier lenses such as Zeiss, but the glass elements are about 2-3 times larger than 35-mm format lenses. This lowers their overall resolution by 15-30%. Numerous MF systems are built around Mamiya lenses. In general, they are comparable to lenses used with Hasselblad systems. MF users report higher satisfaction with Mamiya lenses. By the Hasselblad 1000F started using Zeiss lenses; the flagship 500C became very popular with professional photographers. The newest line of Zeiss lenses are designed for digital sensors with a very flat field. They tend to yield about lp/mm performance, which is borne out by an average of one-full-point lower performance at photodo.com using their MTF-based ratings (3.6/3.9 vs 4.4/4.8). Large format (LF) photographers (4x5 and 8x10) tend to use good quality lenses because they are semi-professionals or professionals. However, the size of the lens elements used in large format systems lowers the overall performance of the lens. The resolution of the center of a large format image will tend to be good to excellent ( lp/mm), while the resolution falls off markedly towards the edge (20-60-lp/mm) which is often an inch, or more, from the center of the lens. An overall rating for lens resolution in LF photography is about lp/mm. The best LF lenses perform at about 80-lp/mm; they have a larger image circle than 35-mm format lenses (1,400 mm 2 vs 20,000 mm 2, a 14-fold difference). Amateur camera photographers in the film era often used Kodak (or equivalent) box or folding cameras from about 1885 to the 1950s (capable of only lp/mm). In the middle of the 20 th -century, amateurs used the Kodak brand point-n-shoot (PnS) cameras such as the Brownie, Hawkeye, Bantam or Kodak Disk Camera, they generally used very simple lenses such as the Chevalier Achromat, capable of only about lp/mm. Beginning sometime in the 1980s, PnS products began using lens coatings to limit flare and internal light scattering, pushing lens resolution as high as lp/mm. Today, many consumer PnS and Compact cameras use lenses made using optical plastic. In all cases, image quality is hampered by handholding, automatic settings and inexperience. Resolution is probably no greater than lp/mm. Current lens development is reemphasizing glass composition (last seen during the turn of the last century). This time, exotic lens shapes are being made using molding and hybrid processes, rather than grinding and polishing. Computer-aided lens designs not thought commercially viable in previous technological eras, can now be manufactured using new processes at a competitive price point. Table 1: Lens Resolution Estimator By Date and Format Professional Amateur - Box Professional Pro & Amateur Cause of Large Format Folding & PnS Medium Format Small Format Date Improvement in lp/mm in lp/mm in lp/mm in lp/mm 1826 base line <20 NA NA NA 1835 Chevalier Achromat 20-ish NA NA NA 1841 Petzval Achromat NA NA NA 1873 Abbe Optics NA NA NA 1886 Zeiss Apochromatic <20 NA NA 1893 Goerz Dagor Achromat NA NA 1902 Tessar hi-contrast NA NA 1925 Leica RF/FPS Elmar NA Rolleiflex MF Zeiss optical coating Hasselblad MF Ektar first SLRs - C, N & Z adv lens coatings cheaper optics LF lens coating point-n-shoot Bold Text indicates format affected by Cause of Improvement in second column. Professional moniker assumes best possible lens; Amateur assumes an average quality lens. KEY: LF = Large Format 4x5, etc.; MF = Medium Format 2¼x2¼, etc.; PnS = Point-n-Shoot compact cameras; Small Format = 35mm rangefinder (1925) and SLR ( ); RF = rangefinder 35mm format; FPS = focal plane shutter; Elmar = Leitz version of Zeiss Tessar high contrast lens; Ektar = Kodak s post WWII coated lens noted for color and contrast; C, N & Z = Canon, Nikon and Zeiss-E/W (east and west); look in Wikipedia for excellent histories and data on equipment manufacturers listed above.

7 p Lens Issues Affecting Resolution There are at least nine different types of lens faults: Defocus Chromatic aberration Spherical aberration Coma (uneven magnification) Astigmatism (non-flat focus) Flare (external light scattering) Dispersion (internal light scattering) or (chromatic dispersion) Misaligned lens elements Dirt and haze on lens surface (light scatter) [Clicking one of the lens faults above will link to the Wikipedia entry on the topic; Google for more information.] The center of the lens is the sharpest region; resolution declines towards the edge of the image circle as defined by the f-stop (iris) diameter. Good modern lenses are not capable of more than 140-lp/mm at the center of the lens, and much less towards the edges of the image. Figure 9b shows the effects of iris diameter on portion of the glass being used at that particular f-stop. Figure 9a & b: Effect of f-stop Diameter on Relative Use of Glass in Lens Fig. 9a, from the tpub.com shows the relative diameter of the f-stop iris, where a larger number defines a smaller f-stop opening; Fig 9b (right) from the sony.ca website, shows how smaller f-stops limit the diameter of light passing through the lens. Using a large lens aperture (smaller f-number) compromises image quality dramatically because the light must use more of the glass in the lens. Small format photography such as dslrs, Compact cameras and cellphones automatically use large apertures to decrease image noise or to make the image possible. Many compact cameras don t use f-stops smaller than f/8, because those exposure modes produce lower image resolution. Large f-stops (f/1.2 to f/3.5) are only capable of below average resolution ( lp/mm). At the edges of the lens glass, aberrations can be extreme such as curved lines or color halos similar to the examples shown in Fig 1d & e. Figure 10: Iris Scattering Effect - In this plot, the resolution performance of a theoretical lens is based on the limitations produced by the diffusion of light from the edges of the iris aperture. The smaller apertures on the left side of the plot (f/16 and f/22) have a greater the proportion of light diffused from the edge of the iris blades. The small apertures (f/16, f/22 and f/32) are often considered best by most large format photographers, because depth-of- field is greater when the aperture is smaller. Note that the large f-stop openings, on the right side of this plot, have the best performance for this one property. When glass use is factored in, the third and forth (f/5.6 & f/8) f-stops have the best performance; see Figure 9. The trade-off between light scattering from the iris edges appears to be optimal at 2-3 stops above the maximum opening (smallest f-number, largest opening). For large format lenses, this is often f/8 to f/11, while for 35-mm format lenses; the optimal range is from f/2.8 to f/5.6. Overly small f-stops will also cause a decrease in image sharpness because of the light scattered from the edge of the iris blades. Figure 10 shows that as the light scattering from the edge of the iris diaphragm blades overwhelms the smaller amount of light through the smaller lens iris openings, image sharpness decreases. Above f/16, image sharpness is decreased significantly.

8 p 8 Smaller f-stops (f/16 - f/45) do enhance depth-of-field. A long field-of-focus is often desirable, but this enhancement is traded for less overall image resolution. Most optical properties are achieved through a trade-off of competing effects. In the absence of working knowledge, moderation is desirable. 4 Using the RPE for Evaluating Resolution in an Imaging System (Camera) There are many factors rolled onto the system Resolving Power Equation (RPE), which is used to predict the resolution of an image made from a system. A "system" is the complete photographic workflow (a) camera - lens axis to film plane alignment, (b) lens - including all the faults listed above, (c) film [native resolution] and (d) processing [both chemical and on-camera automatic settings]. The RPE was developed in the era of film base on experiments and experience of film systems. It is adapted to digital systems with caution. In the basic equation [EQ1] there is one term [1/r] for the media and another [1/r] for the lens. Adding a [photographic] print to the workflow [EQ2] adds a third term for the enlarging lens and a fourth term for the printing paper. Making a print from a negative profoundly lowers the resolution of the image. EQ1 (film and lens only) is used here exclusively for making calculations in this essay. EQ1: 1/R = 1/r [media] + 1/r [camera lens] The FujiFilm Resolving Power equation found in the FujiFilm Data Guide (p102, 1998): Where: (1) R = overall resolving power, and (2) r = resolving power of each component. EQ2: 1/R [system] = 1/r [media] + 1/r [lens] + 1/r [enlarging lens] + 1/r [printing paper] Use EQ2 for calculating the resolution of a photographic print made from film; it is not used here. A print made from the highest resolution color negative film (VR100) will have much less resolution than slide film. Table 2: Selected Film and Lens Resolution Data [to be used in calculation for Table 3 data] Native Film Resolution in ppi Film Resolution 1/r 30% Contrast - No Lens in Path Kodak Ektachrome lp/mm Fuji Astia RAP 45 lp/mm Fuji Provia 100F RDP 55 lp/mm Kodak Ektachrome 100GX 60 lp/mm Kodak Tri-X 400 (2004) 65 lp/mm Fuji Velvia RVP 80 lp/mm Kodak Portra 160NC Color Neg 80 lp/mm Kodak Plus-X 125 (2006) 80 lp/mm Kodak VR100 Color Negative 100 lp/mm Kodak Technical Pan (2004) 142 lp/mm Kodak Panatomic-X 170 lp/mm Lens Resolution 1/r [lens] Lens Cost, in relevant era Dollars Old lens ( ) & LF lens 20 lp/mm 0.05 $ Average Modern lens 40 lp/mm $ Good LF lens 60 lp/mm $ * Very Good lens 80 lp/mm $ ** Excellent 35 mm format lens 100 lp/mm 0.01 $ *** Superior 35 mm lens 120 lp/mm $ **** Exceptional lens 140 lp/mm $ Mythical lens 200 lp/mm Not available for sale Impossible lens 1000 lp/mm Not available for sale * Many 35 mm, medium format and large format prime lenses at optimal f-stop; many first-tier zoom lenses at optimal ** Schneider 150 APO Symmar at f/8, as well as good second-tier prime lenses; handful of zoom lenses at optimal *** Selected first-tier prime lenses at optimal f-stop; Nikon, Canon & Zeiss; very few LF 150 & 180mm lenses **** A handful of first-tier prime lenses at optimal f-stop (f/ ); no LF or zoom lenses One or two 35mm format prime lenses in a generation; extremely rare to find The RPE [equation] can be used to calculate the final image resolution of a photographic system, using data in Table 2 for the respective 1/r values; film values are on top and lenses on the bottom. In Table 3, the RPE was used to calculate final image resolution and loss of image quality, which can range from 15% to 88% of native resolution. Cameras with rigid frames such as 35-mm SLRs and rangefinders bodies, and, medium format (MF) bodies (2¼ x 2¼, or 6 x 6 cm and 2¼ x 2¾, or 6 x 7 cm) have almost flat film planes and rigidly fixed lens-to-film axis. Rigid frame camera bodies will often achieve better results than large format (LF) cameras that require the film and lens axis to be aligned for each series of exposures, using a tool such as the Zig-Align. With careful alignment, view cameras can deliver excellent lens to film plane configurations. Table 3 uses the RPE [equation] to deliver final image resolution for five specific films (film is used here because it is clearer) through lenses of decreasing quality. The point of the data list is to show how the lens influences the final resolution of the image; note the loss reported in the seventh column. The native

9 p 9 resolution of the media is always decreased by the lens, no matter the quality. Note that the 200-lp/mm and 1000-lp/mm lenses will never be found, the data is used to make the point that even if the lens has greater resolution than the media, the lens still degrades the media. Table3: Image Resolution for Four Films Shot thru Lenses of Increasing Resolving Power Kodak Ektachrome 160 (EKT 160) has a native resolution of 35 lp/mm or 1780 ppi digital equivalent Kodak Ektachrome = = 16 lp/mm = 646 ppi 64% loss thru 20 lp/mm lens Kodak Ektachrome = = 19 lp/mm = 948 ppi 47% loss thru 40 lp/mm lens Kodak Ektachrome = = 22 lp/mm = 1121 ppi 37% loss thru 60 lp/mm lens Kodak Ektachrome = = 24 lp/mm = 1236 ppi 31% loss thru 80 lp/mm lens Kodak Ektachrome = = 26 lp/mm = 1316 ppi 26% loss thru 100 lp/mm lens Kodak Ektachrome = = 27 lp/mm = 1377 ppi 23% loss thru 120 lp/mm lens Kodak Ektachrome = = 28 lp/mm = 1423 ppi 20% loss thru 140 lp/mm lens Kodak Ektachrome = = 30 lp/mm = 1512 ppi 15% loss thru 200 lp/mm lens Fuji Velvia (RVP) & Kodak Plus-X Pan (PX) have a native resolution of 80 lp/mm or 4064 ppi digital equivalent Fuji Velvia & Kod Plus-X = = 16 lp/mm = 813 ppi 80% loss thru 20 lp/mm lens Fuji Velvia & Kod Plus-X = = 27 lp/mm = 1355 ppi 67% loss thru 40 lp/mm lens Fuji Velvia & Kod Plus-X = = 34 lp/mm = 1740 ppi 57% loss thru 60 lp/mm lens Fuji Velvia & Kod Plus-X = = 40 lp/mm = 2032 ppi 50% loss thru 80 lp/mm lens Fuji Velvia & Kod Plus-X = = 44 lp/mm = 2258 ppi 44% loss thru 100 lp/mm lens Fuji Velvia & Kod Plus-X = = 48 lp/mm = 2442 ppi 40% loss thru 120 lp/mm lens Fuji Velvia & Kod Plus-X = = 51 lp/mm = 2592 ppi 36% loss thru 140 lp/mm lens Fuji Velvia & Kod Plus-X = = 57 lp/mm = 2903 ppi 29% loss thru 200 lp/mm lens Kodak VR100 Color Negative film has a native resolution of 100 lp/mm or 5080 ppi digital equivalent resolution Kodak VR100 Color Neg = 0.06 = 17 lp/mm = 847 ppi 83% loss thru 20 lp/mm lens Kodak VR100 Color Neg = = 29 lp/mm = 1451 ppi 71% loss thru 40 lp/mm lens Kodak VR100 Color Neg = = 37 lp/mm = 1903 ppi 63% loss thru 60 lp/mm lens Kodak VR100 Color Neg = = 44 lp/mm = 2258 ppi 56% loss thru 80 lp/mm lens Kodak VR100 Color Neg = 0.02 = 50 lp/mm = 2540 ppi 50% loss thru 100 lp/mm lens Kodak VR100 Color Neg = = 55 lp/mm = 2776 ppi 45% loss thru 120 lp/mm lens Kodak VR100 Color Neg = = 58 lp/mm = 2971 ppi 42% loss thru 140 lp/mm lens Kodak VR100 Color Neg = = 67 lp/mm = 3387 ppi 33% loss thru 200 lp/mm lens Kodak VR100 Color Neg = = 90 lp/mm = 4618 ppi 9% loss thru 1000 lp/mm lens Kodak Technical Pan (TP) has a native resolution of 142 lp/mm or 7220 pp digital equivalent resolution Kodak Technical Pan = = 18 lp/mm = 891 ppi 88% loss thru 20 lp/mm lens Kodak Technical Pan = = 31 lp/mm = 1588 ppi 78% loss thru 40 lp/mm lens Kodak Technical Pan = = 42 lp/mm = 2143 ppi 70% loss thru 60 lp/mm lens Kodak Technical Pan = = 52 lp/mm = 2646 ppi 63% loss thru 80 lp/mm lens Kodak Technical Pan = = 59 lp/mm = 2988 ppi 59% loss thru 100 lp/mm lens Kodak Technical Pan = = 65 lp/mm = 3320 ppi 54% loss thru 120 lp/mm lens Kodak Technical Pan = = 71 lp/mm = 3603 ppi 50% loss thru 140 lp/mm lens Kodak Technical Pan = = 83 lp/mm = 4233 ppi 41% loss thru 200 lp/mm lens Kodak Technical Pan = = 125 lp/mm = 6350 ppi 12% loss thru 1000 lp/mm lens 5 - Lens Limits the Resolution of all Imaging Systems In the universe of photographic lenses, most lenses have less resolution than the media they are used to expose. This is understandable. Now that the media is a digital chip where higher resolution costs more, less is usually spent on the lens. In the past, high-resolution film was inexpensive while high quality lenses were expensive. The professional photographer recognizes lens quality is critical to image quality. The lens used to expose photographic media (glass plates, film, CCD/CMOS) has equal mathematical value to the media itself when determining the final resolution of the image. This is easily understood because both RPE terms [1/r] are the same. Should the lens and media have equal resolution, both will contribute equally and lower the resolution of the system to about half of the media s native resolution. It is only the exception lens that exceeds the native resolution of the media, and this is rare. Figure 11 graphically shows the effect of the various lens quality levels on four specific films with a range of native resolutions. The higher resolution films are affected more by lens quality, while low-resolution media suffer less by exposure through lower quality lenses. When this concept is extrapolated to compact cameras, it means image quality is harmed less by low cost lenses than the small chips with small pixel size. Digital cameras have only half the resolution (Nyquist Sampling Theorem) of their sensor; see Appendix 1 below. Lower quality lenses, therefore, have less harm on digital systems. On the other hand, good quality lenses can easily achieve the best from digital sensors. In 35-mm format photography the best lenses are standard focal length prime lenses (35mm, 50mm & 85mm) made by first-tier lens makers such as Canon, Nikon, Zeiss or Leica. The Canon EF 50/1.4 USM prime has a street price of $ Standard lenses (50 mm) can be had for $ , but a modest $400 buys a lot of resolution. The Canon lens is shown below on the left, in Figure 12a.

10 p 10 Figure 11: Effect of Lens Quality in Image Resolution This plot shows the effects of lens quality (y-axis, vertical is lp/mm) on film resolution (x-axis, horizontal ppi of film). Four common films (listed above) are exposed through the theoretical lenses listed above them using the Fuji RPE. The graphic shows that poor quality lenses have a huge effect on lowering resolution, while improving lens quality past about 100-lp/mm has less effect. However, lenses over about lp/mm quality are very expensive; the return for dollar spent is not as great past very good lenses. The films are Kodak Ektachrome 160 (1780 ppi), Fuji Provia (2800 ppi), Fuji Velvia 100 (4064 ppi) and Kodak VR 100 (5080 ppi), right to left. Performance of Prime vs Zoom lens On the digital camera review website their lens evaluation tool lensreviews/ has a wealth of information condensed into an interactive graphic. To make a comparison between an excellent prime lens (Canon 50/1.4) and a kit zoom lens, go to the lens reviews for the (1) Canon 50/1.4 at f-5.6 (full size sensor) and the (2) Canon 18-55F/ set at 35 mm and f-5.6; compare the graphical data at the top of the window, set the f-stop and zoom as recommended. With both lenses set at their optimal f-stops, they show very different behavior. The Canon 50/1.4 prime lens is mostly dark blue out to the edge, while the kit zoom lens is mostly green. Although the actual numbers are not relevant, because the sensor sizes used to evaluate the lenses are different, the lens performance show the value of an excellent prime compared to an average kit zoom lens. The more traditional lens evaluation website, has standard MTF data for a huge selection of lenses, but they have discontinued making the time-consuming traditional (decreasing-size linepairs) MTF measurement for lenses later than about Unfortunately, most of that data is now years old, thus, do not reflect the majority of lenses being sold today. However, the information helps to evaluate historic photographic equipment. The modern lenses that photodo.com rate rely on user evaluations [that often track reality] but are in not measurement-based. Rather they are subjective evaluations made by users. Thus, only the data on the older lenses will fulfill the needs of the RPE. Note on Evaluating Lens Performance using Photodo.com MTF Data: The data reported by Lars Kjellberg photodo.com used one of the pre-digital standard high-end lens evaluation protocols that measured MTF out to 40-lp/mm, across the width of the image circle. Figures 12a & b shows the MTF performance reported from the center (0) out to the edge (21) from the center of the image circle. The MTF performance at the three resolutions used, (a) 10-lp/mm, (b) 20-lp/mm and (c) 40-lp/mm (at 15 degrees from the center) is shown by the red lines on the plots below. The three MTF points (from 10, 20 and 40 lp/mm plots) were harvested using the yellow squares in Fig.12a & b (normal and tangential axis averaged) from the MTF data. When the three data points are plotted in Figures 16-18, 18, a line was drawn through the three points and extended past 30% contrast to predict their absolute performance. The plots from the three Canon prime lenses (straight lines near the diagonal center of the graph) cross the 30% contrast limit line between 95- and 105-lp/mm Spend a few minutes with the photodo.com website checking lens performance. Using <Lens Search>, filter for manufacturer of the lens, which will include both prime and zoom lenses. Compare the performance of the zooms against the prime lenses. It can be seen that prime lenses have the best generic performance, while zoom lenses have a minimum of 15% less resolution because of the numerous compromises made to achieve a fast performance over the focal range of the zoom. Most zoom lenses

11 p 11 being sold in dslr kits perform at about 50-75% of their prime equivalents. MTF is a critical tool for evaluating lenses. It is well explained at nology/mtf.htm and koren.com/tutorials/mtf.html. For more information: Google, MTF lens. Figure 12a: Shows MTF data for the Canon EF USM 50/1.4 prime lens. The figure was constructed from the <photodo.com> website, showing their (older) MTF data. The Y-axis (0-100) of the MTF plots shows residual contrast between line pairs, while the horizontal X-axis (0-21) shows distance from the center of the image circle. Note that wideopen performance plot (left) is much worse than stopped down to f8 (right, of the pair). While the performance at f/8 for both Canon lenses is virtually the same, the wide-open performance is far superior for the Canon 85/1.2. The optimal f-stop for this lens is probably f/3.5 to 5.6. Figure 12b: Shows MFT data for the Canon 85/1.2 prime lens. It was given the very high grade of 4.6; only one lens is given a higher rating of 4.8, the Canon EF 200f/1.8 USM. The 85/1.2 lens even performs better than the Canon 50/1.4 (above). The Y-axis (0-100) of the MTF plots shows residual contrast between line pairs, while the horizontal X-axis (0-21) shows distance from the center of the image circle to the edge. Note that wide-open performance plot (left) is much worse than stopped down to f8 (right, of the pair. The wide-open performance is superior to the 50/1.4. The optimal f-stop for this lens is probably f/2.8 to 3.5; performance will be even better than at f/8, which is 2-3 stops beyond optimal. Figure 12c: Shows MFT data for the Sigma AF zoom lens. Note that the data shown is for f/8. Performance at 50 mm focal length is far better than wide angle (28 mm) and much worse at full telephoto (105mm). The lens is only rated at 2.1 by Photodo.com {MTF Ratings]. This is not the lowest score possible (0.9) but it is quite low. The point being made by the inclusion of this lens in this series of lenses with superior performance is to show (a) a second-tier lens, (b) a zoom lens and (c) the normal rate of resolution drop-off, from the center to the edge of the lens. The optimal f- stop for this lens is probably f/8, maybe even f/11. Thus, we are seeing the best performance of this lens in these plots. Note how the 40-lp/mm plot near the bottom of the graphs (below 30% residual contrast) is very low, showing a marked drop-off of overall sharpness.

12 p 12 Figure 13a & b:contrast between black & white line-pairs and USAF 1951 target - Fig 13a, shows Norman Koren graphic on the change contrast between black and white line-pairs decreased by the lens, film and then both (the system - in the camera). Fig 13b shows a USAF 1951 resolution target used for evaluating the native film resolution. Figure 13a, taken from the Norman Koren website, shows the effects of imposing media, lens and then both together on the contrast of black-and-whitcontrast is at 0% difference; black and white have become equally gray. The upper left corner of Fig 13a shows 100% contrast; the center shows about 50% residual contrast. A point about an inch to the left of 10 2 along the bottom depicts a contrast difference of about 30% between black and white. This is the line-pairs. Note that in the lower right corner, all detail is lost, point where many workers evaluating MTF performance, define the limit of performance 30% contrast limit. Many workers with higher standards, such as Koren, use 50% residual contrast; this effectively lowers the native resolution of the media and the lens. Another method of evaluating lenses is to use USAF resolution targets; see Figure 13b. The method is simple and affordable, but of less value when evaluating overall lens performance. The method is useful for ranking individual lenses, or lenses within a group. Chris Perez and Kerry Thalmann use the method to evaluate many 1980s & 1990 s lenses at The targets shown in Figure 14 are used in SFR image analysis software such as Imatest, and are not used here except for comparison. Figure 14a & b: Image of two Slant Line test charts. Fig 14a (left) depicts the ISO test chart, note the slant line components in the center with the arrows point ing at the features; Fig 14b (right) depicts the Imatest SFRplus chart; it facilitates SFR resolution measurement over the entire image. The slant line target is use by SFR (spatial frequency response) imaging evaluation software such as Imatest. The Influence of Lens Quality on Image Resolution No film or digital sensor can reach the native resolution of the media when exposed through a lens. Even if exposed through the fabled spy lens, which is said be capable of 500-lp/mm, the performance is only about 80-85% of native resolution. The best lenses ( lp/mm) available to you will diminish the native resolution by about 40-55% for film or sensors with the most common resolutions being used today. Figure 15 shows the behavior graphically; the first line up from the bottom (100) shows the behavior of the best lenses, while halfway up is the fabled spy lens (500). The highest lens resolution shown at the top of Figure 15 depicts a mythical lens rated at 1000 lp/mm, which is impossible to achieve. Note that Kodak VR100 (100-lp/mm or 5080 ppi) is only predicted to reached 90% of its native resolution (4600 ppi) using the imaginary 1000 lp/mm lens. Kodak EKT 160 (35-lp/mm or 1780 ppi) performed best in this experiment because lower resolution media are diminished least by poor lenses. However, low-resolution films have much poorer [final] image resolution performance, when compared to the best performing films (VR100).

13 p 13 Figure 15: Degradation of Media Resolution by Lens Quality - The graph shows how film [or CCD] resolution is degraded by the lens being used. The maximum possible resolution of the media (film/ CCD) is listed to right of the vertical colored lines along the x-axis. The curves are a result of calculations using the RPE [equation] for lens of varying quality. Lens quality is plotted along the Y-axis. The lower the quality of the lens the more the maximum resolution of the media is harmed by the lens. The average lens has a resolution of 60- to 80- lp/mm. Kodak EKT160 (1780 ppi) shot through a 70-lp/mm lens has an image resolution of 1200 ppi, a 33% loss. Kodak VR100 (5080 ppi) shot through a 70-lp/mm lens yields an image with about 2000 ppi, a 60% loss of native film resolution. Even a theoretical lens, with 1000 lp/mm resolution (top of plot) can never deliver all the native resolution capabilities of the films shown here. Note that as the film s native resolution increases the curve is less steep, or becomes more flat. Using an Average Lens (60-lp/mm) vs and Excellent Lens (100-lp/mm) The average lens resolves approximately 60-line-pairs per millimeter (lp/mm). If Fuji Velvia RVP (80-lp/mm) was exposed through an average lens, the final system resolution will be about 34-lp/mm, a loss of 57% of the native resolution (1740 ppi digital equivalent). [See table 3.] Using an excellent lens (100-lp/mm) with the same Fiji RVP Velvia color transparency film would produce a system resolution of about 44-lp/mm or about half the native resolution of the film. However, this is roughly a third better performance, when compared to using an average lens. An average standard lens (50 mm) for the 35-mm format can be purchased for $ Using an excellent lens (100-lp/mm) will produce an on-film image resolution a third better over the average lens, but the cost will be about $400. Most professionals consider this good value for the money.

14 p 14 Figure 16: Lens MTF plots: Canon 35-mm format lenses - Canon s best prime lenses, 50/1.4; 85/1.2 and 200/1.8 (not the smaller digital format lenses) have an image circle of about 1.5 compared to a Schneider Symmar APO 150 mm f5.6, large format lens have a 6.5 image circle. These excellent small format primes perform at 90- to 110- lp/mm (2/3rds from center). The performance in the center of the image circle is superior to the edges and probably ranges from 120- to 140-lp/mm. The overall performance of large format lenses, to which they are compared is lower because their size. Canon Lenses: Some of the best performing Canon lenses have been listed in Figure 16 below such as the (a) EF 50mm f/1.4 USM, (b) EF 85mm f/1.2 USM and (c) EF 200mm f/1.8 USM. They are projected to have a resolution of lp/mm at their optimal f-stop (f/5.6). Based on photodo.com MTF data at f/8, and 30% contrast limit, they are delivering lp/mm. These are superior quality lenses at their optimal f-stops. In reality, the crossing points at 30% contrast are most likely somewhat to the right (even better performance). This performance is predicted by the shape of thick purple line (f/11) and thick black (f/5.6, wide-open, for Schneider LF lens) plot lines made using multiple-point point curves for a Schneider APO 150/5.6 lens. It is rare to find MTF lens data plotted in such a manner -- showing the shape of the MTF curve to a low residual contrast. These curves were included in the graphs to show the probable shape of MTF plots, rather than the straight lines used for these predictions. It s possible that both the Canon, Nikon and Leica prime lenses deliver as much as lp/mm if there were MTF data available to the 30% contrast limit.

15 p 15 Figure 17: Lens MTF plots: Nikon 35-mm format lenses - Nikon 35-mm format lenses shown here, 50/1.8; 55/2.8 85/1.8 & 105/2.8 (not the smaller digital format lenses) perform at about 100-lp/mm at optimal f/stop. The performance in the center of the image circle is superior to the edges and could be as high as 140-lp/mm. There performance is compared to the same Schneider 150/5.6 APO used in Figure 14. The overall performance of large format lens is lower because the glass elements used are larger. Nikon Lenses: Note that in the Nikkor/Nikon lens MTF plots in Figure 17 the (a) AF 50mm f/1.8, (b) MF 55 mm f/2.8 and (b) AF 85mm f/1.8 lenses show excellent behavior at f/8, but poor performance wide open (using all the glass in the lens). Their optimal f-stop will be about f/5.6, but data is only available for wideopen and f/8. As with the Canon lenses, their resolution range is lp/mm at the 30% contrast limit. These are excellent quality lenses; show some of the best behavior of the Nikon stable of lenses. Most first-tire lens makers have excellent 35, 50, 85 and 200 mm prime lenses, some rate as high as 4.6 or 4.8 (MTF data) on photodo.com. It is possible that the Nikon primes shown in Figure 17 could deliver as much as lp/mm when used at their optimal f-stop, which would be around f/5.6 based on having fast designs [f/1.4 to f/1.8 wide-open]. In addition, with more data points the shape to the plots lines would be curved similar to the Schneider 150mm APO [thick purple and black plot lines] rather than the straight lines drawn through 3 points. This may further move the 30% contrast point further to the right. Nikkor zoom lenses have a reputation for good performance. The best Nikon zoom on photodo.com has g a 3.9 MTF rating. However, many Nikon zoom lenses have a MTF-based rating of about 3.0 or lower. Recall, that zoom lenses always perform poorer than prime lenses because they must focus light through a range of focal lengths. Zoom lenses have been the beneficiary of modern design and manufacturing improvements. This is especially true of the APS-size lens elements, which are smaller and easier to precision mold.

16 p 16 Figure 18: Lens MTF plots: Leica 35-mm format lenses - Comparison large format and small format (35-mm) lenses; shows a comparison of high quality large format (LF) and high quality small format (35-mm) lenses at the ideal f- stop (f 8 & f11) and wide open (f 2-2.8) with a theoretical lens at f-8. Leica lenses are shown below in Figure 18. The two Leica lenses at f/8 come close to theoretical lens f/8 behavior (dashed thick green line). Note that the 10, 20 & 40 lp/mm data points (four red dots, upper left) almost match the f/8 theoretical lens performance. The straight line estimation of their performance shows 100-lp/mm at the 30% contrast limit. However, when using the shape of the f/8 theoretical lens plot (dashed thick green line), the actual performance may be as high as lp/mm. This is probably also true for the excellent Canon and Nikkor lenses shown in their respective plots. Rating lens quality: prime lenses, such as 35mm, 50mm and 85mm, from first-tier manufactures Canon, Nikon, Zeiss or Leica generally have similar behavior, as can be seen in Figures 16, 17 & 18. This is generally not true of second-tier manufacturers (aftermarket lens) such as Cosina, Sigma, Tamron, Tokina, etc. However, reviews of newer lenses from these manufactures in Popular Photography show better than expected performance. An example of the newer second-tier lens is the Sigma 50/1.4; a DPReview.com lens review can be found at The performance is not as good as the excellent Canon 50/1.4, but it is good enough. Some second-tier lenses may be benefiting from the new lens-element manufacturing technology. Browse the photodo.com website using <Lens Search> for MTF lens data using the Nikon and AF mount filters or Canon and EF mount filters; this will include lenses from all manufacturers not just those by Nikon or Canon. The second-tier lenses are all in the lower rated range (0.9 to 3.5), while first-tier lenses are generally the only ones rated 3.6 to 4.6. Some first-tier lenses will be rated below 3.6, but they will usually be the less expensive versions or wide-angle, medium telephoto or zoom lenses. While most of the Canon, Nikon and Leica lens data shown in Figure 16, 17 & 18 are merely an estimation of performance, it is reasonable to expect such performance because these lenses are considered the best in their class. 6 - Summary and Recommendations It has been shown that the lens is of equal importance to the native resolution of the sensor using the RPE [equation]. Half the resolution in an image, or more, is due to the lens. Use the best lenses you can afford. While the kit [or built-in] lens included with a camera will get you taking pictures right away, better images will be made using average or good quality prime lenses.

17 p 17 Compact cameras and point-and-shoot cameras usually use low-resolution lenses to keep the cost of the system low. The small sensors in the Compact and PnS cameras along with their low quality lenses make them inferior to the dslr. A cellphone image from a camera of equal megapixels to that of a dslr will never be equivalent to a dslr image due to the chip size and lens quality. When using dslrs with full-sized sensors, capable of MP or higher, there is an absolute need for excellent to superior quality lenses made by first-tier manufacturers. Prime lenses are superior to zoom lenses. However, some very high quality (> $1000) zoom lenses [there are very few of these] can almost be equivalent to good quality prime lenses. Excellent prime lenses will always outperform a zoom lens. No matter the quality of the lens, it will degrade the resolution of the sensor, decreasing image quality. Appendix 1 - Note on Digital Cameras It is the nature of digital sensors that double the pixel content is required to be equivalent to the analog domain. The concept is explained by the Nyquist Sampling Theorem, which says that at least twice the digital bandwidth is required to capture analog information in the digital domain. While some folks don t acknowledge the limitations on digital sensors set forth by the Sampling Theorem, a careful examination of any of the common digital camera and lens review venues, from DPReview.com to Popular Photography magazine and Imatest, will show that they all acknowledge the concept and include it in their evaluations. A 24 MP camera has an equivalent number of pixels to the native resolution of common slide film. A 24 MP camera has approximately 4000 x 6000 pixels on its sensor. Film is analog while CCD/CMOS sensors are digital -- they are inherently incompatible. For the purpose of comparison, however, the resolution of film [in line-pairs per mm or cycles per mm] can be made equivalent to pixels by multiplying lp/mm by a conversion factor of 50.8, to produce points of resolution per inch. Using Fuji Velvia film as an example, it has a native resolution of 80-lp/mm at 30% residual contrast. Since 35-mm film, has an image size of 1 x 1.5 (approximately 25.4 x 38) the resolution is multiplied by the conversion factor of Thus, Fuji Velia film has an equivalent image resolution of 4064 x 6096 pixels. It can be said, therefore, that this film and a 24 MP (4000 x 6000 pixels) sensor have an equivalent numbers of points of resolution. It has been shown above, that an 80-lp/mm film (Fuji Velvia = 4064 ppi native resolution) using a good to excellent lens will deliver only about half that resolution, or about 35- to 45-lp/mm resolution, in the image. When the [50.8] conversion factor is applied, the resolution is equivalent to about 2000 ppi in the digital domain. The effect of the lens was calculated using the REP [equation], which uses the (1) native resolution of film and the (2) resolution of the lens used to make the image. The DPReview.com review of a Sony 50/1.4 lens on a 24 MP Sony body reports an image resolution of about 2000 ppi, between f-3.5 and f-10. On the Test Result page, observe that just below the lens resolution graphic is a note [NOTE] in green text that explains that resolution values that are above the Nyquest limit are meaningless. Because the Nyquest frequency is set at about 2000 (for the 4000 pixel chip), the values above 2000 are not real. The picture height of the Sony A900 image sensor used in the evaluation is 24 mm (full-size); therefore, the data is equivalent to the Fuji Velvia data calculated from the REP [equation]. Thus, an image made from a common 24 MP digital system using a good to excellent prime lens is equivalent to a film image made using state-of-the-art slide film with a good to excellent quality lens. The method of evaluation used by DPReview.com is SFR digital image analysis software, a modern technology that is not directly compatible with the older MTF evaluations (see below). They note the Nyquist limit on the graph and explain that although data is reported above the limit, it is meaningless. It is not clear why data is generated above the Nyquest Limit, but one explanation could be the sharpening built into all modern in-camera digital image processing. The sharpening is used to counteract the effects of the low-pass filter used to limit aliasing, which could introduce moiré patters when the pitch of the target (such as fabrics) matches the pitch of the digital chip. All dslr have low-pass filters that cut off resolution at, or just above, the Nyquist limit of the chip. Sometimes the filter is a real filter (lithium niobate, birefringent crystals) other times it is a digital filter built into the processing software; see ing_filter and pp in Digital imaging for Photographers by P. Davies & P. Fennessy, using Google books. With a low-pass filter is place, resolution data reported above the low-pass filter is truly false and meaningless. When Popular Photography makes similar SFR measurements they often report resolution data that is greater (10 to 50% higher) than half the resolution of the chip in the camera being evaluated. That is, they fail to make the same remarks DPReview.com use to recognize that resolution data higher than the Nyquist Limit is not real. This should be noted when using Popular Photography reviews. SFR (Spatial Frequency Response) is the newest method of measuring optical resolution. It can only be applied to digital systems because it evaluates digital image files directly. A common supplier of SFR targets and analysis software is Imatest, developed by Norman Koren. The tool makes MTF evaluations using a completely different type of target (slant line; see Figure 14a & b) and measuring technology

18 p 18 (Fourier Transform of a spectrum of signals) from the older technology. Traditional MTF evaluation were made using the decreasing-size line-pairs target, as shown in Figures 13a &b and a series of contrast measurement made directly from of photographically produced line-pair target using a microdensitometer. While MTF data is comparable, the data presentation is different. Tradition MTF plots show a decreasing resolution, based on residual contrast, while the SFR measurements assume a 50% contrast end point. Thus, analysis done at 30% contrast and 50% contrast are not directly compatible, but within the same universe. Appendix 2 List of Imaging Events Relevant to Lens History Color code for entries: Lens History; Pre-Photography; Film Camera; B&W Photography; Color Photography; Digital Imaging 3000 BC (5000BP) Polished stones were used to magnify (early visual aid) and condense light, about 3000 BC, or earlier Glass was invented in the Bronze Age, and then perfected by the Egyptians BC Greek and Chinese scholars describe the basic principles of optics and camera, circa BC Aristotle writes of darkened room with small hole in one wall, inverted image on opposite wall, BC 1000 AD Reading Stone, a glass sphere use to read by magnified letters was in recorded use around 1000 AD Lens is first described in the Book of Optics by Ibn el-haitam an Iraqi Physicist published in 1021 Camera Obscura published in Book of Optics by Iraqi scientist, Ibn al-haytham, used a pinhole to image in Camera Obscura with a lens, Girolamo Cardano replaced pinhole w/ biconvex lens in 1550s Giovanni Battista della Porta ( ) published first account of Camera Obscura to aid drawing in Telescope - first written mention in Zeeland (Dutch) document, Hans Lipperhey claims a new device in 1608 Galileo made his astrophysical studies using a early telescope in 1610 Newton discovers that white light is composed of colors of light (spectrum) between Reflex-mirror design in a camera obscura was first published in Johann Heinrich Schulze mixes chalk (white base), nitric acid and silver; notices darkening on side of flask exposed to sunlight; first photo-sensitive compound discovered, silver nitrate (AgNO 3 ) in Hall Achromat curved-field lens, uses two glass types (crown & flint) to focus red and blue light in the same place, but because green-light focus point was shifted the resolution was soft, developed about Thomas Wedgwood created Sun Pictures, cameraless shadowgrams ; paper or leather with silver chloride-nitrate; un-fixed; darken with more than a candle; 1802 Royal Society pub by Sir Humphry Davy 1800 Wollaston Landscape lens, first properly designed lens but suffers curved-filed & chromatic aberrations in 1812 Lithography on stone and metal plate (more modern) began in France about 1813 Camera for photography used by Niépce, sliding wooden box camera, by Charles & Vincent Chevalier in 1812 Nicéphore Niépce combines Camera Obscura with photosensitive paper; not fixed, thus not permanent, 1816 First permanent image light-sensitive "bitumen of Judea" on Pewter sheet, Nicéphore Niépce in 1826 Joseph Jackson Lister develops lenses with reduced chromatic aberrations by introducing concept of several lenses, each with a portion of the full magnification formerly required from one lens element, in 1830 Quasi-Zoom lenses were used in telescopes, not true zoom, reported in proceeding of the Royal Society in 1834 Chevalier Achromatic lens, 2 elements cemented together, still found in point-n-shoot cameras, in 1835 Daguerreotype, Louis Daguerre, Ag-I negative on polished copper sheet, devl pd w/ mercury vapor, Fixing is discovered by John FW Herschel, publishes on a successful fixing agent, hyposulphites (Hypo) in 1939 Daguerre licensed Chevalier lens for a wood-body camera designed for quarter-plate under his name in William Fox Talbot publishes how to make Photogenic Drawings, AgCl/-NO 3 crystals in paper, fixed, 1839 Paper negatives (waxed after processing) shown to scientists and hobbyist, see Fox Talbot above, in 1839 Talbotype (Calotype) by William Fox Talbot; AgCl/-N0 3 fixed paper neg. w/contact printing, a pos print 1841 Salted Paper prints (generic name for the Talbot s process) silver salts in paper fibers, fixed, 1841 Petzval Achromatic Portrait lens, first specifically designed photographic lens created in 1841 Carl Zeiss opens his workshop in Jana, Germany to make eyeglasses and microscopes for University 1846 Niépce de St Victor and Louis-Désiré Blanquart-Evrard experiment with albumen on glass plates Albumen Print invented by Louis-Désiré Blanquart-Evrard sensitized egg albumen coated on paper 1850; Printing-Out-Paper technology (POP) where a print is developed by exposure to sun, then fixed and dried; could be further chemically developed for darker image; for many details see Crayon Portraits by itinerate artists, thin POP under-image, chalk or charcoal design layer, 1850 s thru 1900 s Collodion Wet Plates, Frederick Scott Archer, silver-collodion (-Br, -Cl & -I) in ether solvent on glass, 1851 Ambrotype invented by James Ambrose Cutting: an underexposed collodion glass plate negative with a black (cloth) background, combined to produce a visual interpretation that appears as a positive image, 1854 Tintype (Ferrotype) by Hamilton Smith, underexposed neg. on black metal plate, makes positive image First additive color process: 3 exposures thru 3 filters comb d into color image, James Clerk Maxwell 1861 Silver-collodion paper, POP by photographer, Ag- or U-NO 3 in collodion on sized paper introduced about 1864 Ernst Abbe joins Carl Zeiss (Jena) as the main designer in Silver-gelatin process by RL Maddox: AgCl or AgI crystals in gelatin media (water solvent) on glass 1871 Ernst Abbe at Carl Zeiss (Jena) develops Abbe sine condition optics improving optics significantly in 1873 First color print: layers of subtractive cyan, magenta & yellow gel by Louis Arthur Ducos du Hauron in 1877

19 p 19 Rodenstock, Munich Germany, considered superior LF lens maker with their digital (flat field) lenses in 1887 Dry Gelatin Plates, over-the-counter glass plate negatives, thru 1930s, by pro-photogs & press, in Silver-gelatin papers for photographic prints first created about 1880 Print, commercial - Eastman began sensitizing photographic paper using Germany and French papers in 1880 Platinum Print (still salted paper print) was discovered by William Wills in 1873, reached market in 1881 Baryta layer introduced to prints, increases reflectiveness (Dmin) and expands tonal range, about 1885 Kodak releases paper negatives on a roll (paper), processed by Kodak (1888) in 1885 Otto Schott joins Abbe and Zeiss at Carl Zeiss, produces glass equal to Abbe s work, Apochromatic lens developed, corrected for all colors focusing in same plane and coma (all points focusing in same place) in 1886 POP, commercial Printed-Out-Paper is developed w/light, gelatin emulsion on paper 1885; glossy in 1890 Kodak (product name) Eastman Kodak factory sells camera loaded w/ paper film (thru 1889) in 1888 Film - Silver-gelatin coated on cellulose nitrate film created around 1884; plastic film first manufactured, Silver-gelatin print supplants albumen prints (first in 1850), sold pre-sensitized dry in a box around 1890 Paul Rudolph, Carl Zeiss (Jens) develops Anastigmat lens w/2 asymmetrical groups, either side of iris, 1890 DOP silver-gelatin (Ag-Br) papers intro Developing-Out-Paper developed in chemical bath, about Paul Rudolph of Carl Zeiss (Jena) develops the very fast (f/3.5) Planar design, 6-element in 6-groups in 1896 Kodak No1 Folding Pocket Camera used 105 roll film (2¼ x 3¼) on nitrate base (thru 1915) for $10 in Kodak No 3 Folding Camera used 118 roll film (3¼ x 4¼) on nitrate base (thru 1915) for $68 in 1900 The Brownie Camera (thru 1924 w/no 3 to 1934) used 117 roll film (2¼ x 2¼) on nitrate base ($1) in 1900 Carl Zeiss (Jena) renames Anastigmat Series I thru V, Protar, no astigmatism or field curvature in 1900 No 2 Brownie Camera (thru 1924) child s box (cultural icon) used 120 nitrate roll film (2¼ x 2¼) for $2 in 1901 Otto Schott of Zeiss Jena, develop rare earth glass (aka Jena glass) in 1901 Paul Rudolph of Carl Zeiss develops Tessar high resolution & contrast lens; 4 elements in 3 groups in 1902 Zoom lens, first true near-sharp focus design was patented by Clile C. Allen in 1902 Carl Paul Goerz (1886, Berlin) developed the 1-group 3-element Dagor Anastigmatic flat field lens in 1904 Ozobrome, Thomas Manley invents Raydex proportional color pigments in gelatin layers on paper in 1905 Kodak No 4A Folding w/goerz Dagor lens ($110) 126 roll film (3¼ x 5½) nitrate base (thru 1916) in 1906 Kodak begins to study in-house papermaking, and encouraged others such as Am. Playing Card Co., in 1906 Graflex No1A, Folmer & Schwing, USA, first MF (116 roll film) SLR w/ waist-level & focal-plane shutter in 1907 Kodak No 4 Pocket Folding, very large body w/20 lens opt ($83) 123 roll film (4x5) nitrate (thru 1915) 1907 Autochrome, tri-colored starch grains coated on glass was invented by Lumiere brothers, France 1907 Dufaycolor invented by Louis Dufay, mesh of RGB lines on glass, later on motion picture film, in 1908 Finlay Colour Process developed by Clare L Finlay, mosaic of RGB squares on glass plate in 1908 Kinemacolor first color MP process by GA Smith (1906 UK), alternating R, G & G images, released 1908 Kodak opens cellulose acetate factory (used for film base) in Australia about 1908 Kodak announces cellulose acetate Safety Film base (various formulations through time) in Dye Imbibition (absorbing) technology, Trichromatic Plate Pack (3 neg - 1 exp) by Fredric Ives develops in 1911 Schneider Kreuznach optics (German) opens, will make lenses for 35-mm format to large format, in 1912 Kodak builds its own papermaking machine at Kodak Park (1914) first Kodak Park photographic paper in 1915 Technicolor, Process 1, two color (R & G) additive motion picture with 2 simultaneous B&W reels in 1916 Nikon Corp founded and Nippon Kōgaku Kōgyō Kabushikigaisha, renamed Nikon in 1988, opened in 1917 Tri-Color Carbro subtractive color (CMY) pigmented gelatin layer print, Autotype, H.F. Farmer in Technicolor Full Color, Process 4, using 3-strip camera, subtractive (CMY) dye-transfer final print in 1924 Leica I, developed 1913, first 35-mm rangefinder camera with either 5-elm Elmax or 4-elm Elmar lens in 1925 Kodacolor motion picture film by Eastman (not final incarnation) lenticular additive color, 16mm amateur, 1928 Graflex Speed Graphic f/4.5 B&L Tessar or Kodak Anastigmat, wire loop focus (thru 1939) 4x5 & 5x7sht, 1928 Rolleiflex releases its double lens reflex (DTL) medium format (2¼ x 2¼) camera in Kodachrome 2-color additive positive (reversal) color motion picture film tried by Fox Film Co in 1931 Dufaycolor motion picture film, 3-color additive using mesh of RGB lines in 1931 Contax I released by Zeiss Icon (east German) 35-mm SLR rangefinder camera with Zeiss f1.5 lens 1932 Varo mm zoom was the first mass produced zoom lens, made by Bell & Howell for 35-mm MP, in 1932 Ihagee Exakta, (Kine-Exakta) 1 st production 35-mm SLR, 127 roll film (1⅝x2½) w/changeable bayonet lens mm film (35-mm format) acetate base film in familiar pre-loaded daylight-loading cassette by Kodak in 1934 Retina I by Kodak (German-built) using their new daylight-load 35mm cartridge w/ integral Schneider Xenar 1934 Kodachrome (K-14) 3-layered subtractive positive film, stable w/no unused couplers after processing, 1935 Nikkor 50 mm f/3.5 lens (50/3.5) was releases by Nikon, mounted on Hanza Canon (Canon rangefinder) in 1935 Vacuum deposition of lenses coating (1935), by Zeiss, designated T or T* reducing internal reflections & flare, increasing contrast & resolution, not available until 1940, then only in Sweden & Switzerland until after WWII Agfacolor, tripack subtractive color reversal process in 1936 Argus A 35-mm daylight-load cassette camera made for mass consumption ($ ,000 sold) in 1936 Kodachrome has low dye stability from inception (1935) through 1937, improved with 185-yr yellow in HK7 Hasselblad (Sweden) reconnaissance camera w/coated lenses, updating German design for Allies in 1941 Azochrome silver dye bleach print created by Kodak from Eastman s Wash-Off process in 1940 First multi-layer color negative film(s) developed in 1941 Kodacolor, first color print from a color negative film, C-22, red-tone emphasis, thru 1963, began in 1942

20 p 20 Kodak Dye-Transfer, dye imbibition process, gelatin receiver layer accepts 1 of 3 (CMY) dyes, on paper 1945 Carl Zeiss (Jena) assisted by US Army to move into West Germany (Stuttgart) was renamed Carl Zeiss 1946/7 Carl Zeiss (Jena) in East Germany renamed Kombinat VEB Zeiss Jena, labeled Zeiss Jena in west, about 1946 Ektachrome supplants Kodachrome color reversal film, easier processing, blue-tone emphasis in 1946 Ektachrome E1, E2 & E3 released, had poor cyan and yellow dye stability (E3 through 1976), E1 & E2 in 1946 Graflex Pacemaker Speed Graphic w/kodak coated Ektar 101/4.5 (Crown Graphic -1pb) all Press used in 1947 Edwin Land develop Polaroid Model 95, first instant image camera system, B&W only, in 1948 Contax S Carl Zeiss Dresden (east German) first pentaprism 35-mm SLR (prototyped before WWII) in Hasselblad 1600, MF SLR, with focal plane shutter used a Kodak Ektar 80/2.8 lens in 1948/ Nikkor lens quality found equal to Zeiss and Leica multi-coated equivalents in the early 1950s Asahiflex I (Asahi - Pentax) first Japanese 35-mm film SLR w/ waste-level finder using M37 lens mount in 1952 Contaflex by Carl Zeiss (west Germany) release their SLR (single lens reflex, through lens viewing) in 1953 Yashimaflex (Yashica in Japan) medium format (MF) twin-lens reflex (TLR) in 1953 Hasselblad releases 1000F MF SLR body, used the Zeiss Distagon 60/5.6 or the Tessar 80/2.8 in Leica M3 by Leitz (Ur-Leica 1913) advanced 35-mm rangefinder with interchangeable bayonet lenses in 1954 Hasselblad 1000F got rave review from Modern Photography (shot 500 rolls of film & dropped it twice) in 1954 Hasselblad releases its flagship 500C body, with modified leaf shutter, using a range of Zeiss lenses in 1957 Contarex (Cyclops) by Carl Zeiss (west) releases first SLR with integrated light meter in 1958 Canonflex by Canon first Japanese reflex SLR w/ prism and focal-plane shutter 1-month before Nikon F 1959 Nikon F is released, a reflex SLR body with interchangeable lens internal metering (compact & affordable) Multiple-coating developed for lens designs, reach point of penultimate lens performance in the 1960s Hasselblad 500EL (electric) started going into space with NASA, went to the moon on Apollo starting in 1962 Polacolor first instant color process, dye diffusion (Dufaycolor) type, by Polaroid in 1963 Cibachrome silver dye bleach process refined, positives prints from transparencies, Ilford, in 1963 Spotmatic by Pentax a reflex SLR w/ focal-plane shutter, TTL metering and M42 screw lens mount in 1964 Yashica D released with Yashinon lens, MF TLR based on the Rollie, $125 D popular w/ prosumer in 1966 CCD imaging chip, first viable light-to-digital chip, developed by Willard Boyle & George Smith at Bell Labs, High quality lenses become affordable, resolution reaches point of diminishing returns in 1970 s 1975 Flatbed scanner invented by Ray Kurzweil for OCR (becomes Xerox Textbridge 1980) in 1975 Ektachrome E4 with better color dye stability supersedes others in 1977 Schneider begins selling multi-coated (flare suppression) lenses, 1977, completes upgrade of full line 1978 Fujinon begins multi-coated (Electron Beam Coating) lenses, prior they were all single coated, Sony Mavica B&W 0.79 MP, first viable color digital imager, based on video still technology (570x490) in Kodak D-5000, CCD-prototype for all digital SLRs, use KAF-1300, 1.3 MP w/pcmcia, K-mount lenses in Ektachrome E6 claims 250-year dark fading stability for CMY dyes in 1990 Mike Collette invents digital scanback (3750x6000) on seeing Kodak s 6K trilinear CCD, 12-bit ADC, in BetterLight releases Model 6000 Mike Collette develops second-generation scanback (6000x8000) in Polaroid enters Bankruptcy 2001; sold to BankOne 2002; as of 2006, surviving entity only distributing assets Imatest image analysis software developed by Norman Koran in Biogon 25/2.8 lens by Zeiss with Leica M mount, Zeiss claims 400lp/mm in center at f/4, diffraction limit, in 2007 The resolving power of historic film is the subject of another essay in the series Estimating the Resolution of Historic Film Images: Using the Resolving Power Equation (RPE) and Estimates of Lens Quality, which can be found in the VideoPreservation Website Library and VitaleArtConservation website, PDF Gallery.. Tim Vitale Paper & Photographs Conservator Digital Imaging & Facsimiles fax Film [still] Migration to Digital [email protected] Preservation & Imaging Consulting Vitale Art Conservation 2407 Telegraph Ave. Suite 312 Oakland, CA 94612