Viewfinder Optics for Microdisplays

Transcription

1 Viewfinder Optics for Microdisplays For camcorders and digital cameras, a viewfinder consisting of a miniature display and magnifying optics offers some distinct advantages over a directly viewed LCD panel. For example, te magnified miniature display appears muc larger to te viewer s eye, making it easier to see detail. Also, te enclosed optics of a magnified display are not affected by ambient ligt, resulting in excellent contrast even wen used out in direct sunligt. On te oter and, tis approac requires some sort of viewing optics. Fortunately, it is possible to create relatively simple, inexpensive, compact viewing optical systems. Te Simple Magnifier Te simplest magnifier is a positive lens placed a distance less tan or equal to its focal lengt away from te object to be viewed. Suc a system produces a virtual image, tat is, an image tat is only seen wen te viewer looks back into te optical system. In contrast, projection displays produce a real image. A real image can be put on a screen and seen witout aving to view troug te optical system. Angular subtense Lens of focal lengt f Object Virtual Image E s s Object viewed troug magnifier Angular subtense Object V Object viewed directly Optical Product Development, Inc. page 1

2 Te first step in specifying or designing a viewing system for miniature displays is to torougly understand te operation of te simple magnifier. A scematic of one is sown in te figure. As wit any lens system, te magnification is defined to be image eigt divided by object eigt: " magnificat ion = m = = s" s However, te apparent size of te viewed image depends upon te viewing distance (just as any object appears smaller wen seen from a greater distance). To quantify tis, te size of a viewed object is defined by te tangent of its angular subtense: tangent angular subtense = object size object distance Because, for magnifiers, te perceived size of te viewed image depends upon viewing distance, te traditional definition of magnification is not tat useful. Instead, it is common practice to define a quantity called magnifying power: Tangent angular subtense of virtual image Magnifying Power = Tangent angular subtense of object vie wed directly Using te variables defined in te drawing yields: Subtense of virtual image " = s" + E and Subtense of object vie wed directly = V From tese, magnifying power can be calculated: Magnifying Power = " s" + E V " V = ( s" + E) mv = s" + E Optical Product Development, Inc. page 2

3 In order to make tis equation truly useful, it is best to eliminate te variables m and s, wic are bot often infinity (because te object is often positioned at te focal point of te magnifier). Tis is accomplised by first substituting for m in te numerator: Magnifying s" V Power = s, s" + E and ten rearranging te paraxial lens equation: 1 f 1 1 = s s" (were f is te lens focal lengt) into te following form: fs s" =, f s to enable a final substitution for s. Te end product is te relationsip: Magnifying Power = fv fs+ E( f s) Te most common use of a simple magnifier is wit te eye placed rigt up at te lens (E = 0). Also, it is typical to design so tat s = f, wic causes te image to appear to be at infinity, resulting in a sarp image wit a fully relaxed eye, i.e., maximum viewer comfort. Setting E = 0 and s = f, simplifies te expression to: V Magnifying Power = f To obtain a number from tis equation requires arbitrarily setting te viewing distance, V, for te case wen te object is viewed directly. By convention, te value of 250mm (10 inces) is commonly used, resulting in te final, simple expression for magnifying power: 10 Magnifying Power = f Optical Product Development, Inc. page 3

4 Wen designing te viewing optics for a miniature display, it is actually more common to begin by specifying te field of view (angular subtense) defined by te virtual image, rater tan te magnification. Te field of view is ten used to determine te required system focal lengt. Te relationsip between tese quantities can easily be calculated from te equations already given. Again assuming tat te eye is placed directly at te lens (E = 0) and te object is put at te focal point (s = f) and centered on te optical axis, as sown in te figure, Object To Virtual Image Field of view f Definition of field of view ten te equation for (alf) field of view (θ ) becomes: tan(θ ) = f Keep in mind tat θ is te alf te total field of view of te system, and is alf te size of te display. Tis equation can now be arranged to enable te required system focal lengt as a function of d, te full diagonal size of te display: f = d 2tan( θ) Optics Size In a practical viewfinder, oter factors can be just as important as focal lengt. For example, optical system size is a particularly important factor in te design of viewfinders for mass market, portable products suc as camcorders and digital cameras, Optical Product Development, Inc. page 4

5 because as lens diameters increase, so does system size and weigt (and to a certain extent, cost). Tus, in general, it is desirable to te diameter of te optical system. Tere are tree primary design parameters field of view, eye relief and eye box tat are all interrelated, and togeter determine te minimum diameter for te lens system. Eye Relief Eye relief is te distance from te eye to te first surface of te magnifier. Te relationsip between eye relief (E), field of view (θ ) and optics diameter (D) can be approximated using te simple magnifier example, as sown in te figure: To Virtual Image Field of view D/2 E A longer eye relief enables eyeglass wearers to position teir eyes a distance from tis lens and still see te full field of view of te display. However, longer eye relief increases optics diameter. From te drawing, it can be seen tat tis relationsip is D = 2E tan( θ) A typical value for eye relief is 25 mm. Eye Box In a real world design, te viewer sould still be able to see te full field of view of te display, even wen tere is some lateral misalignment between teir eye and te optical axis of te magnifier. Te amount of lateral misalignment tat can occur before some of te image is cut off by te edge of te optics is called te eye box. To increase te size Optical Product Development, Inc. page 5

6 (diameter) of te eye box requires increasing te lens diameter beyond te minimum diameter, D, used in te preceding equations. B D/2 E Definition of eye box Te required lens diameter is obtained by merely adding te desired eye box diameter to te lens diameter calculated from just te axial viewing geometry: D = 2E tan( θ ) + B Tis can be rearranged to give eye box in term of te oter variables: B = D- 2E tan( θ) Like oter design considerations, setting te eye box size is a question of trade-offs. Increasing eye box size clearly makes te display easier for te viewer to use, since it relaxes te tolerance on eye position. But tis may necessitate te use of a more complex and expensive lens system. Tis tradeoff between design complexity and eye box size usually leads to eye box values in te 7 mm to 10 mm range for typical viewfinder applications. Oter Design Factors Tere are a number of oter important design factors tat influence system size, weigt, cost and resolution. Some of te most important of tese include virtual image location, resolution and distortion. Virtual Image Location Optical Product Development, Inc. page 6

7 Wen a magnifier is focused so tat te object is at te focal point (s = f), ten te viewer perceives te image to be at an infinite distance, and collimated ligt enters te eye. Wile tis arrangement delivers maximum viewing comfort, in can create difficulties in some instances. In particular, bifocal wearers may not be able to focus on suc a distant image wen viewing troug te bottom part of teir eyeglasses. Sifting te object (te display) sligtly closer to te magnifier will make te image appear closer, and deliver an image tat is easier for bifocal wearers to accommodate. For viewfinder applications, te typical image distance is in te 1 meter to 2.5 meters range. Sifting te object away from te focal point will sligtly cange te magnifying power formula developed earlier, since tat equation was reaced using te assumption tat (s = f). Resolution and System MTF One arcminute is considered to be te typical angular resolution of te uman eye. If te magnifying power of te viewfinder optics makes an individual pixel in te display appear larger tan tis value, ten te user will be able to discern te pixel structure of te display. Te drawing defines te angular subtense of a single pixel. y x x Definition of pixel angular subtense For a given display pixel count and magnifier field of view, te angular subtense (β) of an individual pixel is: θ β = x, N x Optical Product Development, Inc. page 7

8 were θ x is te full field of view in one dimension and N x is te number of pixels in tat same dimension (an analogous equation can be written for te perpendicular direction, y). As an example, for a QVGA display (320 x 240 pixels) tat subtends a 20 orizontal field of view, eac pixel would subtend an angle of or 3.75 arcminutes. Te viewer would clearly detect te pixelated structure of te display, since eac pixel appears larger tan 1 arcminute. It would be necessary to eiter reduce te magnification (tus reducing te field of view) or use a same sized display wit a iger pixel count in order to remedy tis situation. Of course, tis example assumes tat te optical system itself as an angular resolution sufficient to clearly sow te smallest detail in te object (in tis case, better tan 3.75 arcminutes). One of te best ways to quantify weter or not tis is te case is to determine te modulation transfer function (MTF) of te optics. MTF is basically a measure of te contrast of te optics (wit 100% being perfect) as a function of spatial frequency. MTF can be calculated for a lens system under a specific set of conditions (e.g. magnification and field angle) by most optical design programs. MTF is used to determine system resolution by picking an arbitrary value for te minimum acceptable contrast under tese conditions, and ten determing te igest spatial frequency at wic tat contrast can be obtained. In te case of a miniature display, te finest detail tat needs to be resolved consists of an on/off pixel pair. Te spatial frequency (F Limit ) of tis pair can be calculated using te Nyquist Frequency definition, 1 F Limit =, 2p were p is te size of an individual pixel. For typical displays (suc as te Displaytec Model QDM-0076), te pixels are 12 microns square. Terefore, te limiting resolution in te orizontal and vertical directions is F Limit = 1 2(0.012) = 41.7 line pairs/mm Tus, it is not necessary to evaluate te MTF at iger spatial frequencies tan tis wen evaluating an optical design for a display wit tese pixel dimensions. However, te desired value of te MTF at tis spatial frequency depends very muc upon application. Optical Product Development, Inc. page 8

9 Since obtaining a iger MTF at a given spatial frequency will, in general, require a more complex, sopisticated and (typically) expensive optical system, it is very important tat tis value not be over specified for te application. For example, a viewfinder may require only modest resolution (say 50% at 38 lp/mm) at te center of te image, since it is primarily being used just as a framing device. In contrast, te required MTF at tis same spatial frequency migt be muc iger, across te entire field of view, for optics for a personal monitor. Tis is because tere is important information at te corners of te monitor as well at te center. Distortion Optical distortion is fairly common in non-symmetric optical systems. Distortion is a measure of ow well a square object pattern is reproduced in te viewed virtual image. It sould be noted tat distortion does not effect image resolution, just image sape. Typical examples of distortion and teir nomenclature are sown in te figure; most magnifier systems exibit pincusion distortion. None Barrel Pincusion Types of distortion In general, attempting to reduce optical distortion to very low levels (<1%) in a design will cause oter off axis aberrations (suc as astigmatism) to increase. Tus, it is very important not to overspecify te level of allowed distortion in a viewfinder design. Fortunately, a moderate level of distortion can be tolerated in a viewfinder witout adversely affecting its functionality. Typically, te level of distortion in a quality viewfinder sould not exceed 4%. Basic Magnifier Designs Real world magnifier designs cover a large range in terms of size, complexity, performance and cost, depending on te demands of te application. Tis section briefly reviews some basic configurations tat can serve as a starting point for a viewfinder system design. Asperic Refractive Plastic Optical Product Development, Inc. page 9

10 Te simplest design tat can acieve some degree of performance is a single, asperic plastic lens. Te asperic surface enables correction of sperical aberration, but tere is no color correction. Tis design is very compact and ligtweigt, and minimizes overall package lengt. Wile initial tooling costs for plastic optics can be ig, te unit price drops dramatically in ig volume. In general, a single asperic plastic lens would not provide sufficient performance for camcorder and digital camera viewfinders, but including tis type of component in a more sopisticated design can lower te overall element count, reducing size, weigt and cost. Display Refractive Glass Tis form, wic is a Plossl derivative, consists of two cemented doublets, for a total of four glass elements; all surfaces are sperical. Te design is well corrected for sperical aberration and cromatic aberration, and typically produces relatively low distortion. Tooling costs for sperical glass lenses are low, but unit costs for ig volume production do not drop as steeply for as for molded plastic lenses. Display Optical Product Development, Inc. page 10

11 Refractive Hybrid Tis glass/plastic ybrid design attempts to combine te best features of te previous two configurations. Color correction is provided by te doublet. Te plastic, asperic singlet provides for image quality correction (primarily sperical aberration), wile reducing element count, and minimizing size, weigt and cost. Display Reflective Tis simple reflective system utilizes a single, sperical mirror as te magnifier. A beamsplitter must be used to allow te object to be positioned on axis, and a flat coverglass seals te entire system. Te primary advantage of an all-reflective optical system is tat it is completely free from any cromatic aberration. Also, since te sperical aberration of a mirror is muc lower tan tat of a refractive element of equal power, tis design performs well wit a sperical surface, as opposed to an aspere. One disadvantage of reflective systems is tat tey are not efficient. Te double pass troug te beamsplitter causes a reduction in image brigtness. For example, if te nominal reflectance/transmittance ratio of te beamsplitter is 50/50, ten only 25% of te ligt from te display reaces te viewer s eye after two passes. Optical Product Development, Inc. page 11

12 Display Optical Product Development, Inc. page 12