Measuring Luminance with a Digital Camera: Case History

Transcription

1 Measuring Luminance with a Digital Camera: Case History Peter D. Hiscocks, P.Eng Syscomp Electronic Design Limited [email protected] November 25, 2013 Contents 1 Introduction 1 2 Calibration Setting Exposure Work Flow EXIF Data Step by Step Example Calibration Example Measurement 6 4 Calibration of Neutral Density Filters 7 5 Measuring High Intensity LED 8 6 Measuring LED Parking Lot Luminaire 9 7 Conclusions 9 1 Introduction There is growing awareness of the problem of light pollution, and with that an increasing need to be able to measure the levels and distribution of light. These measurements may be made with a digital camera. Previous papers in this series described the calibration technique for a camera [1] and the construction of a lightintegrating sphere as a predictable source of luminance [2]. This paper shows how the calibration technique is applied to a new camera. The Canon G15 point-and-shoot camera [3] was chosen for this exercise. The G15 contains many of the features expected of DSLR cameras, at a smaller size and lower price 1. The specific feature useful in a luminance measurement are: Figure 1: Canon G15 Camera Raw Format Most point-and-shoot cameras store images in JPEG format. As explained in [1], it is possible to use JPEG formatted images for quantitative measurement of luminance. However, the non-linearity of the image-intensity relation and the limited range of digital values (256 steps) in a JPEG image complicate matters. In a RAW (uncompressed) format image, the relationship between camera settings and luminance is linear and consequently more straightforward to determine. The G15 has the option of storing in JPEG or RAW format. 1 About $350 at Canada Computers in Toronto.

2 Manual Operation The controls for manual operation are readily accessible without stepping through menus. One rotary control selects aperture, another rotary control selects shutter speed. Neutral Density Filter Neutral density filters are useful when photographing high intensity sources. An ND8 neutral density filter is built into the camera. As well, accessory adaptor accepts external 55mm neutral density filters. Battery Power The camera package includes an NiMH battery with charger. A replacement battery is available for about $11. 2 Calibration The relationship between pixel value and luminance is as follows [4]: ( ) t S N d = K c 2 L s (1) f s where the quantities are N d K c Digital number (value) of the pixel in the image Calibration constant for the camera t Exposure time, seconds f s Aperture number (f-stop) S ISO setting L s Luminance of the scene, candela/meter 2 The digital number (value) N d of a pixel is determined from an analysis of the image, using a program like ImageJ [5]. Pixel value is directly proportional to scene luminance L s. It s also dependent on the camera settings. To calibrate the camera one photographs a known luminance, plugs values for luminance, exposure time, film speed and aperture setting into equation 1. On then solves for the value of the calibration constant K c. It is then be possible to use the camera at other settings of exposure time, film speed and aperture setting. One determines the pixel value in the image and then runs equation 1 in the other direction to calculate an unknown luminance. 2.1 Setting Exposure Figure 2: Light Integrating Sphere The measurement image must be properly exposed. Luminance images consist of a high intensity source surrounded by a relatively dark background. As a consequence, a normal camera exposure meter tends to read low. The light source is then over-exposed. There are three methods of determining the correct exposure. Maximum Pixel Value The pixel values are represented inside the camera as binary numbers. The range for the pixel value N d is from zero to N max, where: N max = 2 B 1 (2) where B is the number of bits in the binary numbers. For example, for a 16 bit raw image, the range of values is from zero to = For an 8 bit JPEG image, the range of values is considerably smaller, from zero 2

3 to = 255. In order not to lose information in the image the exposure must be adjusted so that the maximum pixel value is not exceeded. So, if you find a pixel value of in a raw image, it s overexposed. To determine the correct exposure, take one or more images, and then determine the pixel values. This is a trial-and-error method, and it s labour intensive. Spotmeter Exposure Value If you have a spotmeter, such as the Minolta model M, you can use that to determine the appropriate camera settings. For this to work, the field of view of the spotmeter - 1 field of view in the case of the Minolta M - must be less than the source. For physically large sources (HID lamp, for example) this is possible. For a single LED the source is probably smaller than the spotmeter field of view and this approach won t work. Assuming the spotmeter will work with the light source (the aperture of the light-integrating sphere is one example), then the exposure value EV is given by: where: 2 EV = N2 t (3) EV Exposure Value from spotmeter N Aperture setting (f-stop) t Exposure time, seconds Notice that ISO setting is not included in this equation. A wide variety of combinations of Aperture Setting and Exposure Time apply to the same Exposure Value, so we can choose one and calculate the other. Example: What is the appropriate shutter speed for an exposure value of 12 when the aperture setting is F4.0? Solution: Rearrange equation 3 to solve for exposure time t: t = N2 16 = 2EV 4096 = = 1/256 so a suitable exposure time is 1/250 second. Wikipedia has a convenient table [6]. For example, an exposure value of 11.9 was obtained for the aperture of the light integrating sphere. Rounding this off to 12 and consulting the table, suitable exposure values include 1/4000 sec at F1.0 through to 1/60 second at F8.0. Shorter exposure values are appropriate for a moving target or where camera shake may be a problem. Image Histogram The image histogram is a graph showing the number of pixels on the vertical axis versus the pixel value on the horizontal axis. For an image that contains only black and white pixels (no grey) image, the histogram contains two spikes: the height of the leftmost spike is proportional to the number of black pixels. The height of the rightmost spike is proportional to the number of white pixels. With care, this can be used to set the correct exposure. Figure 3 shows an example. The black spike is at a Figure 3: Image Histogram pixel value of zero, so it lines up with the Y axis and is difficult to see. The white spike is at a pixel value of 192, so most of the pixels in this image have a value of zero or 192. If there were grey pixels, at some value between 0 and 192, these spikes would be smeared out over a horizontal region. 3

4 The G15 camera can display a histogram of the image on its display. The technique is then to identify the histogram spike associated with the light source and ensure that it is not saturated, that is, not up against the right-hand boundary of the histogram. It helps to zoom into the image, so that the light source occupies as much of the image as possible. This increases the height of the corresponding spike on the histogram. Shooting the aperture of the integrating sphere so that the aperture occupies a large area in the image results in a histogram that is easy to interpret. The histogram peak representing the aperture luminance is quite obvious. In the field, especially for small diameter LED sources, the source occupies a small area of the image and the histogram in the camera is difficult to interpret. The ImageJ histogram measurement can use a log vertical scale to make the source stand out from the background noise. Furthermore, the ImageJ histogram indicates the maximum pixel value, which must be kept under to avoid over-exposure. The G15 has three settings for the exposure meter: wide, intermediate and narrow. It helps to set the camera exposure meter to the narrowest possible setting. 2.2 Work Flow The image analysis program ImageJ cannot accept Canon raw format (.cr2 formatted) files. They must be converted to.tiff format. Here we show the steps to do that conversion. The image work flow for the Canon G15 is shown. A similar work flow will apply to other Canon cameras. Configured to generate RAW files in.cr2 format, eg img_0020.cr2. img_0020.cr2 dcraw -w -4 -T img_0020.cr2 img_0020.tiff convert img_0020.tiff -colorspace Gray output_0020.tiff output_0020.tiff, 16 bit black-white imagej Histogram, profile, average or pseudocolour You can remove the intermediate file (img_0020.tiff in this example) to save disk space. 2.3 EXIF Data EXIF data (also known as metadata) is information that is attached to an image. It contains photo parameters such as exposure interval, aperture and ISO speed rating that is required in automating the conversion of image data to luminance. This is enormously convenient in practice. It enables one to collect a series of images without having to manually record the camera settings. One can return to images after the fact and determine settings from the EXIF data. A complete listing of EXIF data is found using the command line program exiftool. For example, the command exiftool myfile.jpg lists the EXIF data for myfile.jpg. The EXIF data is not necessarily carried through the processing steps of section 2.2 above, so it is adviseable to use the metadata information in the first file in the sequence, the raw file from the camera, format cr2. More information on EXIF Data is in [1]. 2.4 Step by Step Here we assume the light integrating sphere as a source, and the Canon G15 camera. 1. Using a luxmeter, measure the illuminance at the sphere aperture. Calculate and note the corresponding luminance. 4

5 2. Photograph the aperture, using care to ensure that the image is properly exposed (Section 2.1 above.) 3. Note the values of ISO setting, exposure time and aperture number. Or use exiftool to extract that data from the image file. 4. Using the workflow of section 2.2, convert the image to.tiff format. 5. Load the image into the image analysis program (ImageJ or equivalent) and determine the average pixel value of the aperture image. (a) Start ImageJ. (b) Open the raw image file (eg, output_0569.tiff). (c) If the image needs to be scaled, place the cursor in the image and hit either the + or key to scale the image. This has no effect on the maximum, minimum or average value of the pixels, it just spreads out the image, which may make it easier to work with. (d) Select the area of interest for example with the ellipse tool. (e) Under Analyse -> Set Measurements select the measurements required (eg, average grey scale). (f) Select Analyse -> Measure. A measurement window pops up or, if the measurements window is already open, adds a line with the measurement of the average pixel value. 2.5 Example Calibration Determine calibration luminance. The illuminance of the light integrating sphere aperture, measured with 2 different luxmeters, is 1590 lux. Then the luminance is: L = E π = 506 candela/metre2 Prepare to photograph the calibration source. Using the Minolta M spotmeter, we measure the Exposure Value of the aperture at We arbitrarily choose an exposure of 1/60 second. Round the Exposure Value up to 12 and consult the EV chart of reference [6], then the appropriate aperture is F8.0. Alternatively, we could re-arrange equation 3 enter the value of exposure time t, and solve for N, the aperture: N = t 2 EV = = 7.98, 8.0 When we analyse the image, we find the maximum pixel value is about 44,000, well below saturation at So the combination of 1/60 second and F8.0 seems to work well. Convert image to black & white format. Using the workflow of section 2.2, we convert the image to.tiff format, obtaining the following files: Image File Name File Size, MBytes Original Raw img_0020.cr Tiff Colour img_0020.tiff 77.9 Tiff Black & White img_0020-final.tiff 26.0 For a RAW format image, the original.cr2 format is a reasonable size. The.tiff images can be very large. The Tiff Colour image is an intermediate step and can be deleted once one has obtained the final image, to save storage space. Determine the Pixel Value of the Image Using the procedure in item 5 of section 2.4, determine the average value of the pixels in the calibration image. Figure 4(b) shows the image of the light integrating sphere aperture, with an area selected for measurement. Figure 4(c) shows the result of that measurement: the average pixel value N d in the calibration image is

6 (a) Main Menu (b) Image (c) Measurement Results Figure 4: ImageJ Screenshots Determine the Calibration Constant of the Camera We are going to rearrange equation 1 (page 2) to solve for the calibration constant K c. The known quantities in that equation are: N d Digital number (value) of the pixel in the image t Exposure time, seconds 1/60 sec f s Aperture number (f-stop) F8.0 S ISO setting 100 L s Luminance of the scene, candela/meter candela/m 2 K c = N d fs = = t S L s 1/ This is the calibration constant for the camera, and applies at other values of exposure time, aperture number and ISO setting. It can be used in equation 1 to determine luminance from the pixel value in an image. 3 Example Measurement Now that we have the calibration constant or the camera, we can measure the luminance of a light source. We ll run a confirmation measurement of the light-integrating sphere aperture. This time, we set the camera exposure time to 1/250 second, the aperture to F4.0 and the ISO to 80. The lens zoom is set to some arbitrary position that creates a reasonable sized image. We measure the average pixel value in the image as Summarizing: N d Digital number (value) of the pixel in the image t Exposure time, seconds 1/250 sec f s Aperture number (f-stop) F4.0 S ISO setting 80 K c Camera calibration constant 3400 Now we rearrange equation 1 to solve for the luminance: L s = N dfs = tsk c 1/ = 510 candela/m2 (4) The calibration value of the aperture is 506 candela/m 2, reasonably close agreement. 6

7 4 Calibration of Neutral Density Filters What is the maximum luminance that can be measured by the camera? Using equation 4 for luminance, we substitute the maximum pixel value and the extreme values for camera settings: N d Digital number (value) of the pixel in the image t Exposure time, seconds 1/4000 sec f s Aperture number (f-stop) F8.0 S ISO setting 80 K c Camera calibration constant 3400 L s max = N dfs = tsk c 1/ = candela/m2 (5) We know from previous measurements that the luminance of an LED can easily reach 157,000 candela/m 2, which would be overexposed at these camera settings. Consequently, we will need a neutral density filter to reduce the luminance to a level that can be photographed properly. The Canon G15 has an internally selectable neutral density filter which is ND8, that is, it is supposed to reduce the image brightness to 1/8 (0.125) of its original value. We also tested external neutral density filters ND2, ND4 and ND8 2. We explored two different methods to measure the effect of a neutral density filter: Constant Settings Keep the camera settings (ISO, F#, shutter speed) constant. Measure the pixel value of an image with and without the ND filter. The pixel value should decrease by the same factor as the ND filter. This method requires that the pixel value change over a very wide range. In practice, the results were inconsistent, possibly due to the wide range of exposures. Adjustable Settings Adjust the camera settings so that the histogram remains constant, that is, the camera exposure settings compensate for the effect of ND filter. The change in exposure value is then equal to the effect of the ND filter. In practice, the measurements were consistent over two runs with different camera settings. This method has another advantage: it s possible to approximately determine the attenuation of the ND filter very quickly. Keep the ISO and aperture setting constant. Adjust the shutter espeed, with and without the ND filter, so that the histogram peak is at the same value. Then the value of the ND filter is equal to the ratio of the filter speeds. For example, suppose the shutter speed without the ND filter is 1/200 second. With the filter, adjusting to match the first histogram, it is 1/25 second. Then the filter has an attenuation factor of 8: ND8. For increased accuracy, you can measure the average pixel values in the two images (they should be similar values) and use their ratio as a correction factor. In both cases, we photographed in manual mode, image format RAW, converted to monochrome TIFF format. We then used ImageJ to measure the average value of pixels in the image, and used those values as correction factors for the shutter speed ratios. First run: ISO 400, F8.0, reference image 1/200 second. Second run: ISO 100, F4.0, reference image 1/200 second. The measurement results for these filters were as shown below. Nominal Actual Variation Deviation Attenuation Attenuation (2 measurements) from Nominal 8 (Internal) 7.61 ±0.6% 5% 2 (External) 1.92 ±0.5% 4% 4 (External) 3.69 ±3.5% 7% 8 (External) ±4% +26% The measurement results are sufficiently consistent over two runs to create confidence the values are reliable. The internal ND8 filter is more consistent and closer to the nameplate value than the external filter. 2 The filters were a set, manufactured by Digital High Definition, obtained from EBay, price approximately $15. They are 55mm in diameter and connect to the Canon G15 with a lens adaptor Kiwifotos LA-58G15 and 55 to 58mm filter adaptor ring. 7

8 5 Measuring High Intensity LED (a) Image: ND8 (b) Image: ND2 with ND8 (c) Image: ND4 with ND8 (d) Profile: ND8 (e) Profile: ND2 with ND8 (f) Profile: ND4 with ND8 Figure 5: LED Photographs Figure 5 shows test photographs of a high intensity LED source 3. Camera settings for the unsaturated image (figure 5(c)) were set to minimize exposure, as follows: N d Digital number (value) of the pixel in the image t Exposure time, seconds 1/3200 sec f s Aperture number (f-stop) F8.0 S ISO setting 80 K c Camera calibration constant 3400 ND 4 Neutral Density Filter, External 3.69 ND 8 Neutral Density Filter, Internal 7.61 Modifying equation 4 to incorporate the effect of the neutral density filters, the luminance of the source is estimated at: L led = [ ND 4 ND 8 N dfs 2 ] [ ] = = candela/m 2 (6) tsk c 1/ The LED source is so bright that it causes significant (but fortunately, temporarly) loss of vision - even when viewed off axis. For the measurement, it was mounted with a tube to constrain off-axis light and protect the eyesight of the camera operator. The images show the effect of the internal and external neutral density filters. The single ND8 internal filter, and the combination of the ND8 internal filter with an ND2 external filter, are not sufficient to prevent overexposure. The images show black spots which are symptomatic of over-exposure 4. As well, the pixel values of the profiles of those images exceed (2 16 1) at various points. The combination of internal ND8 filter and 3 LedEngin part number LZ4-40CW10, available from Newark Electronics. 4 Possibly numeric overflow of 16bit numbers? 8

9 external ND4 filter are necessary to prevent overexposure. Notice the enhanced detail in image (c), where the four LED chips can be seen clearly. The corresponding profile in (f) has a maximum value of 60650, so that image is not overexposed. 6 Measuring LED Parking Lot Luminaire (a) Overview (b) Closeup Figure 6: Parking Lot Luminaire Figure 6(a) shows a local Toronto parking lot, illuminated with LED fixtures. Subjectively, the fixtures appear to create significant glare. One of the fixtures was photographed from an oblique angle, simulating the viewpoint of a viewer at some distance. Figure 6(b) shows a closeup of that photograph. Analysis in ImageJ gives an average pixel value of The peak value is Using the lower of these two numbers, the settings for the camera are summarized as follows: N d Digital number (value) of the pixel in the image t Exposure time, seconds 1/3200 sec f s Aperture number (f-stop) F8.0 S ISO setting 100 K c Camera calibration constant 3400 Neutral Density Filter, External None Neutral Density Filter, Internal Off Calculating the luminance of the fixture using equation 4, we have: L led = N dfs = tsk c 1/ = candela/m2 (7) The reasonable threshold for glare [7] is about 1500 candela/m 2. This luminaire exceeds that level by a factor of 21. Notice that the pixel value is not far from its maximum value, so the camera settings are on the verge of requiring at least an ND2 filter. On axis is much brighter. A photograph taken below the same fixture required an ND8 filter to avoid overexposure. That measurement shows a luminance of 295,000 candela/m 2. 7 Conclusions A digital camera is a useful tool in measuring luminance. The camera must be able to shoot in manual mode, produce images in RAW format and accept external neutral density filters. The camera must be calibrated for luminance. One option is to use the equipment described in [2]. ImageJ is an excellent tool for image analysis. Most used features in this application: magnify the image, calculate average pixel value, and determine a profile line through the image. 9

10 It is difficult to predict a priori what should be the settings of the camera. Some images may require no neutral density filters. Others may require multiple filters. (The high intensity LED source described above required an ND32 filter, that is, the combination of ND8 and ND4 filters.) An unknown image should be photographed at several different exposures, ie, with different neutral density filters. It would be much more convenient if the camera were directly connected to a computer and the analysis software could run in near real-time. Then measurements on the image could then be made directly in the field. For example, there is no explicit indication of maximum pixel value on the camera display 5. However, various ImageJ analyses show the maximum value in the image, and this is critical to avoid over-exposure. It may be possible to use the command-line program gphoto2 as the basis for operating the Canon G15 camera in tethered mode, connected to a laptop computer [8]. Photo Credit Canon G15 Camera References [1] Measuring Luminance with a Digital Camera Peter Hiscocks, 16 Sept [2] Integrating Sphere for Luminance Calibration Peter Hiscocks, 30 October [3] Canon PowerShot G15 Quick Review [4] Exposure Metering: Relating Subject Lighting to Film Exposure Jeff Conrad [5] ImageJ Wayne Rasband [6] Exposure Value [7] Maximum Luminances and Luminance Ratios and their Impact on UsersâĂŹ Discomfort Glare Perception and Productivity in Daylit Offices Andrew Scott Linney Thesis, Victoria University of Wellington, Master of Building Science, http: //researcharchive.vuw.ac.nz/bitstream/handle/10063/651/thesis.pdf? sequence=1 [8] The gphoto2 Reference (the man pages) 5 Overexposure is indicated in playback by modulating the brightness of the overexposed area. This can be easy to miss when the source is a small section of the image. 10