How to extrapolate camera settings from earlier subjects to new subjects
If you are working on a new planetary subject, just take a look at what exposures you used on
previous planets, compare the new subject's surface brightness (typically expressed in mag/sq
arcsec) to that of the previous. From above, if we didn't know what exposure to use for Saturn, but
had previously photographed Mars and Jupiter, we could look at the three surface brightnesses
(given above) and "guess" that the lum exposure and gain would be between 48-62ms at a gain of 12
(Mars is X8.3 higher surface brightness, Jupiter is X2.8 higher). The expected values for RGB
exposures will be in the ballpark, but not as close as will be the lum exposures. The typical
integrated brightness for a planet is, of course, visible light magnitude, not narrow filtered light
(remember that planetary magnitudes may be negative, some of them are bright). If we know the
present diameter of the planet (in arcsec), we can find the projected surface area (in sq arcsec). The
surface brightness is given by:
Mag(sb) = Mag(vis) + 1.09 X ln(Area)
Or you can just take a look at the excellent reference site, www.calsky.com. Click on Planets, click on
the desired planet, click on Apparent View/Data, go toward the bottom of the page, under Physical,
and look for Surface Brightness.
Skynyx 2-0 Characteristics
I recently made a few measurements on my Skynyx 2-0 camera. Using the measurement methodology
layed out in Astronomical Image Processing (Berry and Burnell), I collected flats (1/2 scale exposure),
darks, and bias frames, at 7.5 and 15fps, over a range of "Gain" settings, to calculate the read noise
and conversion as a function of the "Gain" setting in Lucam Recorder. The measured read noise is
about 5 to 6 e- rms (1/2 the value that I expected). I also made measurements at a Gain setting of 12,
at 30 and 60fps. The conversion was relatively insensitive to the frame rate (~5% lower measured at
60fps) and read noise still measured in the 5 to 6 e- rms ramge (lower than expected). The
conversion of the camera, expressed in e- / ADU is shown in the below figure.
The values shown are on a 8/12b basis. If you make the measurements using 16b images, and use
the raw image data to calculate the conversion, you'll get values that are 1/16 of the values shown.
This is because the internal ADC is 12b (4096 total ADU), while the full resolution image file is 16b
(65536 values). These values, and the knowledge that most planetary scenes are satisfied with 7 to
8b of depth, would lead you to choose 9 < Gain < 18. I arrived at the conclusion (see earlier reported
gains) that the Gain should be set between 10 and 15 as a "best" compromise between exposure
time, frame rate, dynamic range, and noise.
Darks frames (bias corrected) of duration from 0.5 to 10 seconds led to the conclusion that the dark
noise for the Skynyx 2-0 is ~ 1 e-/p/s (shorter frames show almost X2 this level, asymtotically
approaching as the exposure increases, bring the value of each pixel above 0.0). This level of dark
noise makes it clear that this, and most other uncooled cameras, aren't designed for long exposure
work. Photos of Uranus and Neptune, or use as a guide camera, requiring a couple seconds of
exposure, do fine, but otherwise, use a cooled camera for longer exposures. It should also be noted
that the e- collection rate drops almost linearly until you get over midscale. The drop decreases until
the onset of saturating large numbers of pixels, then the collection rate drops rapidly, as would be
expected (look at the histogram of the preview window, keep the average at, or just above mid
scale, and by all means, keep the maximum well below saturation).
Capturing a low noise image
So what do these values of gain, read noise, and dark current have to do with planetary imaging?
Camera noise, and most importantly read noise, does affect the image, especially when we shorten
the exposure (increase the frame rate) in an attempt to reduce blur due to atmospheric turbulence.
If we reduce the exposure too much, the read and dark noise will become a substantial portion of
the total noise, and we'll have problems bring out details without artifacts caused by the noise. How
short can we make the exposures and still have the (unavoidable) Poisson noise associated with
photons from the object swamp the total image noise? Below are the applicable equations and an
example.
The number of photons per second, from an object, that are collected by a telescope through a filter
is given by:
Np (photons per second) = ( 10 ^^ ( 8.0 - (mag / 2.5) ) ) * B * A
were the ^^ represents raising 10 to the power of the quantity within the brackets, mag is the total
magnitude of the object (in the imaging band of interest), B is the bandwidth, in nm, of the filter
being used, A is the area (square meters) of the scope aperture (we really need to consider the
aperture efficiency here, but I'll neglect it).
To convert to electrons per second, Ne, multiply Np by k * Qe, were k ~0.9 to 0.95, Qe is the average
sensor quantum efficiency over the band of interest.
Now we have the total number of e-/sec, due to the object getting into the camera. We need to know
the number of e-/sec per pixel, so we need to calculate the area of the subject, and use the image
scale of the system to calculate the number of pixels containing the subject. Then just divide the
total number of e-/sec by the number of pixels over which it is spread.
As an example, Saturn is about 18" across, neglecting the rings (which do contribute to the total
magnitude, but less so than the body of the planet). The area is 255 square arcsec. The focal ratio I
use is f/40, yielding a scale of 0.15"/pix with the Skynyx 2-0 pixel size of 7.4u. This means that the
body of Saturn is spread across 11300 pixels. If we plug the numbers into the equation for Np (lum
filter has B of 250nm, 10" scope has A of 0.05 square meters, visual magnitude of Saturn is about
0.6), we get Np = 7.1 X 10^^8 p/sec, then using Qe=50% and letting k=1 (a 5 or 10% over estimate), we
get Ne = 3.5 X 10^^8 e-/sec and 31150 e-/sec per pixel. Thats a lot of e- per pixel, in fact, most of the
pixels would saturate in less than a sec.
We aren't interested in what happens with a 1 second exposure, we want to know something about
really short exposures at high frame rates. We need to look at the camera noise. The read noise I
measured was 6e-, the dark noise was 1e-/sec/pix. The total noise of the subject is approximately
total object noise = sqrt ( Ne + read noise^^2 + dark noise^^2 ), object noise = sqrt ( Ne )
We want the S/N, as defined by object electron count / total noise electron count, to be high (If there
were no camera noise, the S/N would be sqrt (Ne) ). The S/N will be acceptably high if the object
electron count swamps the read and dark noise electron count. If we set the criterion that the total
noise be less than 1% greater than the object noise alone, this will certainly be the case. For the
noise values given (31150e-/sec/pix, 6e-, 1e-/sec/pix) we find that the Ne exceeds the other two by
the desired amount if the exposure time, t > 59msec. I noted earlier that the lum exposure for Saturn
required 55-60msec to achieve the desired 1/2 scale on the exposure histogram, so I guess that we
have a reasonable exposure, and S/N for this case. If you run a shorter exposure, not only is the
histogram insufficiently filled (under exposed), but the camera noise will become a more important
fraction of the total noise, hence reducing the object S/N. If we had a high read rate camera with a
higher Qe, and lower read/dark noise (especially read noise), we could run a shorter exposure, get
an adequate histogram fill, and retain the acceptable S/N. I haven't found that camera as this writing,
but I keep looking. The EM CCD cameras, if they get the read rates up may satisfy this objective.
Similar calculations for Jupiter (mag = -2.4, B=250nm, A = 0.05 square meter, Planet Area = 1257
square arcsec, Qe=50%) yields Ne = 5.6 X 10^^9 e-/sec, and we have (for my camera and scope) 55870
pixels involved, or 1.0 X 10^^5 e-/sec/pixel. The exposure required to keep the total noise less than
1% greater than the object noise for my camera is 18.5msec. The suggestions that I gave earlier for
lum exposures on Jupiter was 17msec. I guess that the total noise will be about 1.1 or 1.2% greater
than the object noise alone at that exposure (I want to keep the frame rate up to 60/sec, so I take the
slight S/N hit).
If you are working on a new planetary subject, just take a look at what exposures you used on
previous planets, compare the new subject's surface brightness (typically expressed in mag/sq
arcsec) to that of the previous. From above, if we didn't know what exposure to use for Saturn, but
had previously photographed Mars and Jupiter, we could look at the three surface brightnesses
(given above) and "guess" that the lum exposure and gain would be between 48-62ms at a gain of 12
(Mars is X8.3 higher surface brightness, Jupiter is X2.8 higher). The expected values for RGB
exposures will be in the ballpark, but not as close as will be the lum exposures. The typical
integrated brightness for a planet is, of course, visible light magnitude, not narrow filtered light
(remember that planetary magnitudes may be negative, some of them are bright). If we know the
present diameter of the planet (in arcsec), we can find the projected surface area (in sq arcsec). The
surface brightness is given by:
Mag(sb) = Mag(vis) + 1.09 X ln(Area)
Or you can just take a look at the excellent reference site, www.calsky.com. Click on Planets, click on
the desired planet, click on Apparent View/Data, go toward the bottom of the page, under Physical,
and look for Surface Brightness.
Skynyx 2-0 Characteristics
I recently made a few measurements on my Skynyx 2-0 camera. Using the measurement methodology
layed out in Astronomical Image Processing (Berry and Burnell), I collected flats (1/2 scale exposure),
darks, and bias frames, at 7.5 and 15fps, over a range of "Gain" settings, to calculate the read noise
and conversion as a function of the "Gain" setting in Lucam Recorder. The measured read noise is
about 5 to 6 e- rms (1/2 the value that I expected). I also made measurements at a Gain setting of 12,
at 30 and 60fps. The conversion was relatively insensitive to the frame rate (~5% lower measured at
60fps) and read noise still measured in the 5 to 6 e- rms ramge (lower than expected). The
conversion of the camera, expressed in e- / ADU is shown in the below figure.
The values shown are on a 8/12b basis. If you make the measurements using 16b images, and use
the raw image data to calculate the conversion, you'll get values that are 1/16 of the values shown.
This is because the internal ADC is 12b (4096 total ADU), while the full resolution image file is 16b
(65536 values). These values, and the knowledge that most planetary scenes are satisfied with 7 to
8b of depth, would lead you to choose 9 < Gain < 18. I arrived at the conclusion (see earlier reported
gains) that the Gain should be set between 10 and 15 as a "best" compromise between exposure
time, frame rate, dynamic range, and noise.
Darks frames (bias corrected) of duration from 0.5 to 10 seconds led to the conclusion that the dark
noise for the Skynyx 2-0 is ~ 1 e-/p/s (shorter frames show almost X2 this level, asymtotically
approaching as the exposure increases, bring the value of each pixel above 0.0). This level of dark
noise makes it clear that this, and most other uncooled cameras, aren't designed for long exposure
work. Photos of Uranus and Neptune, or use as a guide camera, requiring a couple seconds of
exposure, do fine, but otherwise, use a cooled camera for longer exposures. It should also be noted
that the e- collection rate drops almost linearly until you get over midscale. The drop decreases until
the onset of saturating large numbers of pixels, then the collection rate drops rapidly, as would be
expected (look at the histogram of the preview window, keep the average at, or just above mid
scale, and by all means, keep the maximum well below saturation).
Capturing a low noise image
So what do these values of gain, read noise, and dark current have to do with planetary imaging?
Camera noise, and most importantly read noise, does affect the image, especially when we shorten
the exposure (increase the frame rate) in an attempt to reduce blur due to atmospheric turbulence.
If we reduce the exposure too much, the read and dark noise will become a substantial portion of
the total noise, and we'll have problems bring out details without artifacts caused by the noise. How
short can we make the exposures and still have the (unavoidable) Poisson noise associated with
photons from the object swamp the total image noise? Below are the applicable equations and an
example.
The number of photons per second, from an object, that are collected by a telescope through a filter
is given by:
Np (photons per second) = ( 10 ^^ ( 8.0 - (mag / 2.5) ) ) * B * A
were the ^^ represents raising 10 to the power of the quantity within the brackets, mag is the total
magnitude of the object (in the imaging band of interest), B is the bandwidth, in nm, of the filter
being used, A is the area (square meters) of the scope aperture (we really need to consider the
aperture efficiency here, but I'll neglect it).
To convert to electrons per second, Ne, multiply Np by k * Qe, were k ~0.9 to 0.95, Qe is the average
sensor quantum efficiency over the band of interest.
Now we have the total number of e-/sec, due to the object getting into the camera. We need to know
the number of e-/sec per pixel, so we need to calculate the area of the subject, and use the image
scale of the system to calculate the number of pixels containing the subject. Then just divide the
total number of e-/sec by the number of pixels over which it is spread.
As an example, Saturn is about 18" across, neglecting the rings (which do contribute to the total
magnitude, but less so than the body of the planet). The area is 255 square arcsec. The focal ratio I
use is f/40, yielding a scale of 0.15"/pix with the Skynyx 2-0 pixel size of 7.4u. This means that the
body of Saturn is spread across 11300 pixels. If we plug the numbers into the equation for Np (lum
filter has B of 250nm, 10" scope has A of 0.05 square meters, visual magnitude of Saturn is about
0.6), we get Np = 7.1 X 10^^8 p/sec, then using Qe=50% and letting k=1 (a 5 or 10% over estimate), we
get Ne = 3.5 X 10^^8 e-/sec and 31150 e-/sec per pixel. Thats a lot of e- per pixel, in fact, most of the
pixels would saturate in less than a sec.
We aren't interested in what happens with a 1 second exposure, we want to know something about
really short exposures at high frame rates. We need to look at the camera noise. The read noise I
measured was 6e-, the dark noise was 1e-/sec/pix. The total noise of the subject is approximately
total object noise = sqrt ( Ne + read noise^^2 + dark noise^^2 ), object noise = sqrt ( Ne )
We want the S/N, as defined by object electron count / total noise electron count, to be high (If there
were no camera noise, the S/N would be sqrt (Ne) ). The S/N will be acceptably high if the object
electron count swamps the read and dark noise electron count. If we set the criterion that the total
noise be less than 1% greater than the object noise alone, this will certainly be the case. For the
noise values given (31150e-/sec/pix, 6e-, 1e-/sec/pix) we find that the Ne exceeds the other two by
the desired amount if the exposure time, t > 59msec. I noted earlier that the lum exposure for Saturn
required 55-60msec to achieve the desired 1/2 scale on the exposure histogram, so I guess that we
have a reasonable exposure, and S/N for this case. If you run a shorter exposure, not only is the
histogram insufficiently filled (under exposed), but the camera noise will become a more important
fraction of the total noise, hence reducing the object S/N. If we had a high read rate camera with a
higher Qe, and lower read/dark noise (especially read noise), we could run a shorter exposure, get
an adequate histogram fill, and retain the acceptable S/N. I haven't found that camera as this writing,
but I keep looking. The EM CCD cameras, if they get the read rates up may satisfy this objective.
Similar calculations for Jupiter (mag = -2.4, B=250nm, A = 0.05 square meter, Planet Area = 1257
square arcsec, Qe=50%) yields Ne = 5.6 X 10^^9 e-/sec, and we have (for my camera and scope) 55870
pixels involved, or 1.0 X 10^^5 e-/sec/pixel. The exposure required to keep the total noise less than
1% greater than the object noise for my camera is 18.5msec. The suggestions that I gave earlier for
lum exposures on Jupiter was 17msec. I guess that the total noise will be about 1.1 or 1.2% greater
than the object noise alone at that exposure (I want to keep the frame rate up to 60/sec, so I take the
slight S/N hit).
| Planetary Photo Techniques (page 4, Updated 4/6/08) This page continues with the Skynyx Camera & Lucam Recorder |
