http://www.clarkvision.com/photoinfo/night.and.low.light.photography
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Contents
Introduction
Night photography of City Scenes
Very Low Light Imaging
Light Intensities Under Different Lighting Conditions
A Moonlit Scene
Astronomical Imaging
Discussion
Improving Photon Collection
Other Digital Cameras
References
Introduction
Night and low light photography places some very demanding constraints on photography. Compared to daytime photography, night and low-light photography in the digital age hits new limits, including noise due to photon statistics, read noise from digital sensors, with limits imposed by transmission of optics and the quantum efficiency of detectors.
Night photography of City Scenes
Night photography of cities with a DSLR is easily done with relatively short exposure times, as shown in Figure 2. Use a low ISO setting to reduce noise, an f/stop that gives enough depth of field and sharp images, and a few second exposure time. After each exposure, check the image and its histogram to see if more exposure is warranted. I usually do a wide range of exposures, like in the situation in Figure 2 where I did images from 1 second to 60 seconds. That way I could use a short exposure to maintain detail in the brightest portion of an image, and the longest exposure gets the faint detail. Multiple images could be combined if desired for recording a very high dynamic range. In this case, I found a single 20-second exposure to be ideal for the mood I wanted.
Very Low Light Imaging
In order to show the effects and methods in very low light imaging, which might be scenes away from city lights with the light of the moon, or simply stars, or dark overcast nights, and astronomical imaging of faint stars, galaxies and nebulae, we need a controlled environment. A controlled environment was set up in a darkroom where experiments were conducted over several days. These tests illustrate how faint a signal can be recorded with a DSLR. The DSLR used was a Canon 1D Mark II. The performance of the camera used in the test is documented in Reference (1). In general, the best low light performance for this camera was found to be at ISO 1600 where the read noise is only 3.9 electrons and the gain is 0.81 electrons/camera 12-bit DN. Every convert electron is the result of the capture of one photon. With this calibration, the number of photons detected at each pixel in any image can be directly measured and the noise modeled. This allows us to explore the optimum for low light imaging methods with cameras like the 1D Mark II.
Some of the issues with very low light imaging is noise from dark current over long exposures. So one strategy developed by amateur astronomers using DSLRs for astrophotography is to do many shorter exposures. But every exposure suffers from read noise. Read noise is a constant amount of noise added to every image. You would like your signal to be large compared to the read noise, so read noise doesn't impact image quality.
Noise in an image is:
N = (P + r2 + t2)1/2, (eqn 1)
Where N = total noise in electrons, P = number of photons, r = read noise in electrons, and t = thermal noise in electrons. Noise from a stream of photons, the light we all see and image with our cameras, is the square root of the number of photons, so that is why the P in equation 1 is not squared (sqrt(P)2 = P). Both the total photons counted, P, and the thermal noise, t, are functions of exposure time. P is directly proportional to exposure time. Thermal noise is is related to dark current. Dark current is usually expressed as electrons/second, and the noise is the square root of the electrons, so t is proportional to the square root of the exposure time. If thermal noise dominated images after a certain time, then shorter exposures added together might be a better strategy.
A low light experiment was set up in a darkroom. A long exposure tests up to 30 minutes detected no residual light in the room. A white LED was covered with aluminum foil containing a pin hole, and a piece of white paper diffused the light. The light was pointed toward the direction of the target and using the known reflectances of squares on the target, equation 2 (below) was used to measure the light intensity illuminating the target. The light was measured at 0.00016 lux through the green filter of the Bayer filter. The full image of the test target is shown in Figure 3a, and the strip used for measurements and comparisons is shown in Figure 3b. The measured light recorded by the camera is shown in Table 1 along with a noise model using equation 1. The read noise for the camera is 3.9 electrons, and the dark current is 0.25 electrons/second at the temperature of the test (room temperature. 68 degrees F). For how these values were determined, see Reference 1 ( Procedures for Evaluating Digital Camera Noise and Full Well Capacities; Canon 1D Mark II Analysis http://www.clarkvision.com/imagedetail/evaluation-1d2/index.html).
Figure 3a. The full image view of the test target for the 0.00016 lux light test.
This is a 632 second exposure at ISO 1600 with a Canon 1D Mark II with a 50mm
lens at f/1.8.
Figure 3b. A 623 second exposure of a target illuminated by only
0.00016 lux. The 1D Mark II camera was operating at room temperature
and ISO 1600 with a 50mm f/1.8 lens. This image has had no stretching
or processing other than raw image conversion in Photoshop
with default settings, then the two rows cropped
from the full image and down sampled about 4x.
The width of the image is the full height of the original image.
| Color Chart Patch |
Average Intensity (Photons) | Photon Rate (Photons per pixel/second) | Measured Noise (electrons) | Noise Model (electrons) |
| A | 749.4 | 1.21 | 26.9 | 30.3 |
| B | 494.9 | 0.794 | 24.0 | 25.8 |
| C | 288.7 | 0.463 | 22.7 | 21.4 |
| D | 148.5 | 0.238 | 21.4 | 17.9 |
| E | 60.6 | 0.097 | 21.2 | 15.2 |
| F | 19.4 | 0.031 | 16.8 | 13.8 |
Now let's examine working at lower levels by shortening the exposure time. There are three methods in use in the astrophotography community: 1) sum many short exposures to give a total long exposure time, 2) a few longer exposures summed together to give a total long exposure time, versus 3) single long exposures. An example of the difference between the two methods is shown in Figure 4 and Table 2. When working at low light levels, an important step is dark subtraction. Dark subtraction examples are shown later in Figure 5. At low levels digital cameras typically have a non uniform zero level as well as different offsets from pixel to pixel. But by taking a few images with the lens cap on, one can record what these offsets are, and use the dark images to subtract off the offset. This was done in the images in Figures 4 and 5.
Figure 4 shows a 623 second exposure of the test target sub-section with the gray patches studied labeled A, B, C, D, E, and F. Each test is called a set. Sets 1 and 2 are single exposures, while set 3 is six 10-second exposures combined with ImagesPlus 2.5 using sigma clipped median. Median combine reduces noise spikes due to hot pixels or spikes due to cosmic rays and other effects. A simple average of the images produces nearly the same result in this case. Note how the noise in set 3 appears similar to that in set 2. Square E is faintly seen showing that the camera is showing image detail while detecting less than 6 photons per pixel! The more interesting fact is, shown in set 3, that each exposure was detecting on average only 0.97 photons per pixel for patch E. With a read noise of 3.9 electrons, 0.97 electrons is only 25% of the noise. The reason we can see patch E is because the eye is integrating many pixels, averaging the noise. To first order, Figure 2 set 2 appears close to set 3, but set 3 shows fewer large noise spikes. The multiple exposures, when combined with dark frame subtraction, eliminates large noise spikes.
 Figure 4. The test target from Figure 3. Set 1 is the same image from Figure 3b, but with a linear conversion. Each image is multiplied by the factor indicated. For example, you can recover the 16-bit tif file numbers by converting the image to 16-bit and dividing set 1 by 4, set 2 by 41.52, and set 3 by 234. The multipliers applied to each image is effectively an increase in ISO, or "digital ISO." Set 1 has an equivalent ISO of 3200, set 2 = ISO 66,450, and Set 3 = ISO 374,000! |
|
Now let's push a little fainter. Figure 5 shows Sets 2 and 3 from Figure 4 for reference. Set 4 shortens the exposure time to 1 second, showing 60 exposures combined using ImagesPlus 2.5 sigma clipped median combine, with dark subtraction (after the combine), and Set 5 shows just one of those 60 exposures, also with dark subtraction. Note the number of photons detected on each patch. In Set 4, patch E is faintly visible but not as well as it is in Set 3. Even though the total exposure time is the same, the read noise from each exposure in Set 4 contributes to the noise in the final image. The fact that patch E is faintly visible in Set 4 shows that the camera can record only 0.1 photon per pixel per image and if enough images are added, image detail can be recorded. Obviously, as the photon count rises, the image quality improves. Patch D in Set 4 appears distinct even though only 0.24 photons per pixel per frame are recorded. Patches C and B show more cleanly despite recording only 0.46 and 0.79 photons per pixel per frame. All patches in Set 4 have noise 3 to over 100 times fainter than the read noise of 3.9 electrons per pixel per frame. While 0.1 photons per pixel per results in detectable image detail, totaling about 6 photons, patch D, at 0.03 photons per pixel per frame, totaling only 1.9 photons, does not show a detection. A reasonable conclusion is that the total signal after combining multiple images should be greater than the read noise for one frame.
 Figure 5. The equivalent ISO's for the single frame images are: Set 2 = ISO 66,450, and Set 5 = 3,883,000. |
Light Intensities Under Different Lighting Conditions So what are typical light levels one might encounter in real-world conditions? Table 4 shows the relative brightness scale and common subjects (derived from Reference 5). Several units are used in the table, the stellar magnitude equivalent of the illuminating source, the Luminance at the Earth's surface, and what the camera exposure would be to properly expose an 18% gray card. The brightnesses of astronomical objects is measured in stellar magnitudes, with the star Alpha Lyra forming a reference = 0 at all wavelengths. It is an absolute scale whose units are the brightness of the star Alpha Lyra. The Stellar Magnitude is a log scale with one magnitude equal to the fifth root of 100, or 2.51188643, and larger numbers mean fainter. Table 4
Stellar Luminance at Camera
Magnitude Earth's surface Exposure
(lumens/sq. meter) Time on 18%
(lux) gray card
Sun overhead -26.7 130000 1/600s f/8 ISO100
Full daylight (not direct sun) -24 to -25 10000-25000
Overcast day -21 1000 1/4s f/8 ISO100
Very dark overcast day -19 100 1/4s f/4 ISO200
Twilight -16 10 1s f/4 ISO400
Deep twilight -14 1 3s f/2 ISO400
1 Candela at 1 meter distance -13.9 1.00 3s f/2 ISO400
Full Moon overhead -12.5 0.267 3s f/2 ISO1600
First or Last Quarter Moon, overhead -10.0 0.027 30s f/2 ISO1600
Total starlight + airglow -6 0.001 775s f/2 ISO1600
Venus at brightest -4.3 0.000139
Total starlight at overcast night -4 0.0001 970s f/1 ISO3200
Sirius -1.4 0.0000098
0th-mag star 0 0.00000265
1st-mag star +1 0.00000105
6th-mag star +6 0.0000000105
A camera's light meter can be used to measure lux. The formula is
comes from the definition of ISO (see Reference 2, and references therein)
lux = 12.4 * pi * f/#2 / (R * t * exposure_time * ISO), (eqn 2) where f/# is the f/number of the camera lens, exposure time is in seconds, ISO is the ISO speed, R = reflectance of the target, t = lens transmission, and pi = 3.14159. Equation 2 can be simplified with some assumptions. If we assume white paper with 90% reflectance (use a stack of several sheets), R = 0.9, and assume the optical transmission, T = 0.7, then Equation 2 reduces to: lux = 62 * f/#2 / (exposure_time * ISO), (eqn 3) For example, I measured the exposure time on white paper in full sunlight at 1/3000 second at f/8, ISO 100. Equation 3 gives the lux from the sun as 119,000, agreeing within 10% of the value in the above Table 4. If you want to use an 18% gray card, the factor 62 becomes about 310. A Moonlit Scene As a test of a low light situation and what can be recorded in a real scene, a country road outside of a city with distant mountains was imaged when it was illuminated by the moon 1 day after first quarter. The predicted illumination was 0.06 lux. Assuming an average reflectance of 18%, and finding an exposure of 10 seconds produced a well-exposed scene, equation 2 gives 0.06 lux, in agreement with prediction. By reducing exposure time, we can observe how image quality is reduced due to fewer photons and the camera's read noise. Images were recorded in raw and jpeg mode. with exposures range from 10 seconds to 1/20th second on a Canon 1D Mark II camera at ISO 1600, using a 50mm f/1.8 lens. Raw data were converted with a linear conversion using ImagesPlus 2.5. A second raw conversion was also done with the same software and a standard transfer curve. The linear data were used to determine the number of photons detected. At ISO 1600, the gain is 0.81 electrons/12-bit camera DN, and the maximum number of photons (4095 camera DN) is (4095*0.81=) 3317. The read noise at ISO 1600 is 3.9 electrons (Reference 1)
The number of photons detected in patches A-E is given in Table 5. Figure 7 is the same as Figure 6, without the text and boxes to show the highest signal-to-noise ratio image detail. Figure 8, a 1-second exposure shows that a decent image can be acquired with only a few tens of photons. Less than about 10 photons per pixel still forms a color image where significant detail can be recognized. But at this level, non-uniformities in the dark level become a limitation (Figures 10, 11). For such low levels, a dark frame subtraction can push limits even lower (Figure 12). In Figure 12, where photons counts are similar to and less than 1 photon per pixel per frame, image detail is still visible but only with significant noise. Note the average signal-to-noise ratio per pixel is about 0.25. Finally, combining a few of these short exposures again provides a better image (Figure 13).
Table 5
Compare the noise in Figures 8 and 13. Figure 8, with an exposure time of 1 second in one exposure, has less noise than the 3.2 second equivalent of the image in Figure 13. The noise model (equation 1) shows Patch B of Figure 8 has a signal-to-noise ratio of (38.2/sqrt[38.2 + 3.92 + 0.25] =) 5.2 and in Figure 13 of (sqrt(64)*1.9/sqrt(1.9+ 3.92 + 0.05] =) 3.7. Thus, the visible noise in the two images is what we should expect. This illustrates that while you can dig signal out of the noise with multiple exposures, longer exposures can produce better results. If the sensor had no read noise and no thermal noise, the images would be photon noise limited and Figure 8 would have a signal-to-noise ratio of 6.2 and Figure 9 would have 11. For images with a few tens of photons per exposure, signal is sufficient that read noise becomes insignificant and the sensor is essentially photon noise limited. This means that to improve the signal to noise further in this imaging situation would require a sensor with higher quantum efficiency. The Canon 1D Mark II sensor quantum efficiency is about 38% (Reference 2), so improvements of up to almost 2.6 are possible, and a little more with improvements in optics transmission. Another way to deliver more light is to use a faster f/ratio lens. Comparing results from the moonlight scene and the much lower light level darkroom test shows an interesting difference in the photons per pixel. The higher light level moonlit scene requires higher photons/pixel per frame to see image detail. This is because of the complexity of the moonlit scene, and has nothing to do with light levels. In such complex, real world scenes, practical limits are a half to 1/3 of a photon per pixel per frame. Astronomical Imaging The ultimate in low signal detection is imaging faint stars, galaxies, and nebulae. Reference 2 shows that the signal received from the reference star Alpha Lyra by the Canon 1D Mark II camera through the green passband and a 500 mm f/4 lens is about 1,1950,000 photons/second through the Earth's atmosphere (with average extinction). From that, we can compute how many photons fainter stars would record (Table 6). The photons/minute = 60*A/(10^(0.4*M)), where A = the 1,1950,000 photons/second from Alpha Lyra with that 5-inch aperture lens, and M is stellar magnitude. Table 6
Recording surface brightness is another issue for detecting light from galaxies and nebulae. The 5-inch aperture (125 mm) 500 mm lens on a 1D mark II camera gives 3.38 arc-seconds/pixel with 8.2 micron pixel spacing (= 3600 *arc tangent(0.0082/500 ~ (0.0082/500)/206265). Adding a 1.4x TC reduces that to 2.42 arc-seconds/pixel. The angular area is 11.4 square arc-seconds per pixel at 500mm and 5.86 square arc-seconds per pixel at 700mm (500 mm with the 1.4x TC). Now we can compute the photons the camera plus lens would record for different surface brightnesses (Table 7). Table 7
Note: Photons/minute are converted photons in the sensor, not photons incident on the sensor. Discussion Using the photons/minute in Table 7, you can compare the expected total photons in an astronomical image to the results in Figure 6 to 13 to see what kind of signal and noise you might expect when imaging astronomical objects. Faint parts of galaxies are in the surface brightness 24 and 25 magnitudes per square arc-second range and fainter. Galaxies tend to have surface brightnesses in the 17 magnitudes per square arc-second in their cores with fainter outer parts, while nebulae such as that in the Pleiades (M45) runs about 20 magnitudes per square arc-second and fainter (see References 3, 4). The bright core of the Orion Nebula, the Trapezium, in M42 has surface brightnesses in the 16 to 17 magnitudes per square arc-second range. Images that reach to 21 to 22 magnitudes per square arc-second show the beauty of many galaxies and nebulae, but the signal may appear a little noisy at the low end. Longer exposures reaching 24 magnitudes per square arc-second will appear smoother, but can require hours of exposure. Improving Photon Collection There are several ways for the camera to detect more photons. 1) Improve the transmission of the optical system. If the optics had 100% transmission, the improvement would be less than a factor of 2. 2) Improve quantum efficiency. I measured the 1D Mark II's QE as 28% (Reference 2), so about a 3.6x improvement is possible. Back-side illuminated CCDs have QEs in the 90+ % range, so ~3x is feasible. 3) If you do not need color, the Bayer filter could be removed. The bandpass of the green filter, for example, is about 0.077 microns, and the width of the sensor is about 0.7 microns, so a factor of about 9 for bandwidth and at least another 10% for transmission would result in a 10X improvement. The raw sensor ISO would then be on the order of 16,000 instead of 1600! But the large wavelength range would require new lenses as most lenses are not color corrected from the UV to the infrared where the sensor responds. It would also give unusual black and white response (more like black and white infrared film). There are applications were such full wavelength range imaging is done, as in low light night vision video applications. But for color imaging, the low noise DSLRs are working amazingly well and the tests here show low noise DSLR sensors could compete in some of those situations. Other Digital Cameras The examples on this page used one high-end model digital camera. But the low light performance of this camera is similar to other digital cameras as shown in Reference 6 ( Digital Camera Sensor Performance Summary). The astrophotograph of the Pleiades (M45) in Reference 4 ( Surface Brightness of Nebulae in M45) was taken with a Canon 10D digital camera. The digital camera of choice for amateur astronomers is currently the Canon 20D or 30D due to the relatively large pixels, low read and low thermal noise, and spectacular astrophotos are also being obtained with Nikon DSLRs. Cameras with small pixels collect fewer photons per pixel: see Reference 7 ( The f/ratio Myth and Digital Cameras), and Reference 8 (Digital Cameras: Does Pixel Size Matter?). A demonstration of pixel size in night photography is illustrated in Reference 9 ( Digital Cameras: Does Pixel Size Matter? Part 2: Example Images using Different Pixel Sizes) which shows increased noise (due to fewer photons being collected) with the camera with small pixels. For cameras with small pixels, one would need to take many short exposures (a few seconds each) and add the images together. To see the performance of digital cameras to the faintest light, see Figures 6 and 7 in Reference 6 ( Digital Camera Sensor Performance Summary). Because the electronic sensors in digital cameras have high quantum efficiency compared to film, and because electronic sensors do not suffer from reciprocity failure as does film, large pixel digital cameras can detect lower light levels in shorter time than film. For example, see Reference 10 for a 20 minute total exposure time comparison between film and digital. Conclusions Digital Cameras are capable of detecting small numbers of photons and making credible detections of image detail. If multiple images are added together, or multiple pixels are added, photon rates of less than 1 photon per pixel per frame can still result in detectable image detail. However, for beautiful smooth images, hundreds of photons are required. References 5) Clark, R.N., Visual Astronomy of the Deep Sky, Cambridge University Press and Sky Publishing, (book of 355 pages), 1990. 6) Digital Camera Sensor Performance Summary http://www.clarkvision.com/imagedetail/digital.sensor.performance.summary 7) The f/ratio Myth and Digital Cameras http://www.clarkvision.com/photoinfo/f-ratio_myth 8) Digital Cameras: Does Pixel Size Matter? http://www.clarkvision.com/imagedetail/does.pixel.size.matter 9) Digital Cameras: Does Pixel Size Matter? Part 2: Example Images using Different Pixel Sizes http://www.clarkvision.com/imagedetail/does.pixel.size.matter2 10) A 20 minute total exposure time comparison between film and digital: http://www.aoc.nrao.edu/~whwang/misc/D200_vs_film
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