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Camera Calibration

00:00:11;14 So in the camera lecture, we saw that cameras have a
00:00:14;20 bunch of different properties that are important to know.
00:00:17;21 And the camera manufacturers give you a spec sheet,
00:00:22;06 with a lot of these properties of cameras. But in this
00:00:26;29 tip, I want to show you how you can measure a whole number
00:00:30;26 of these things yourself to make sure that they actually
00:00:34;12 conform to the specifications, and also that there are certain
00:00:38;01 features that are not listed here but that may be important to you
00:00:41;18 that you can quite easily measure. I have here a camera, and
00:00:46;06 this is just a camera that belongs to that spec sheet.
00:00:49;28 I have a c-mount on the camera with a cap, so that at the
00:00:54;03 moment, no light is reaching it. With this capped camera, no
00:00:59;11 light is reaching this CCD and we can see what the dark image
00:01:04;04 looks like, and we can do some measurements on the dark
00:01:07;03 image. When I now snap an image, first thing that I see
00:01:13;16 is that the size of this image is 2048x2048 pixels.
00:01:20;13 And that is exactly the same as promised on this spec sheet, so
00:01:24;11 we are getting the pixels that we paid for. Now to make this a
00:01:29;15 little bit easier on the software, I'm going to take a subreading.
00:01:33;13 And this spec sheet says that it can take subareas, yes?
00:01:43;03 And I'll be working with a subregion of 512x512 pixels.
00:01:53;12 Now what you already see now is that the picture doesn't look
00:01:56;29 black, but kind of grainy. So there's a certain type of noise.
00:02:01;24 And we assume that most of this noise is the readout noise.
00:02:06;11 And to now see what this noise is, the best thing that you can do
00:02:11;25 is to measure. And I've set the software up so that it will measure
00:02:16;25 the mean, the average of these pixel values, and the standard
00:02:21;06 deviation. And here we see that we have a mean of about 100.
00:02:26;04 And a standard deviation of about 3. And the mean in this
00:02:30;13 case is the offset, so the manufacturer put the lowest pixel
00:02:35;13 value a certain number higher than zero so that we can
00:02:39;10 actually see this noise and it's not clipped. And the standard
00:02:43;12 deviation is a measure for the readout noise. When we now
00:02:49;26 go live, we see a couple of things. One is that all this noise is
00:02:56;06 changing, we see some lines moving and most likely those
00:03:01;25 lines are some kind of very small amount of electronic noise
00:03:07;03 happening in this system. Now, a test that you always will want
00:03:13;11 to do is to run a series of images with no light reaching the camera
00:03:20;28 to see if the baseline, that zero level, is the same in all of them.
00:03:27;05 So when I now set this up to take a hundred time points and
00:03:33;26 acquire them, first of all you see how incredibly fast this is.
00:03:37;29 We have set an exposure time of 3 milliseconds, and this whole series
00:03:43;02 actually takes place in something like 300 milliseconds.
00:03:47;00 So we have a hundred images in 300 milliseconds.
00:03:50;23 Then we use this tool here to measure all the intensities
00:03:57;27 and standard deviations in these 100 images. And what we see
00:04:02;21 here when we now scroll through the list is that we have a mean
00:04:07;04 of roughly 101 and stays more or less constant, indicating that our
00:04:15;23 baseline stays nice and flat. And also the standard deviation
00:04:19;17 stays nicely roughly 2.9 - 3. So in this point in time,
00:04:27;13 we know that this reflects the readout noise, but we don't know yet
00:04:31;11 how digital numbers relate to photons. And so to express
00:04:37;07 the readout noise the way we want it, in photoelectrons,
00:04:39;29 we will need that photon conversion factor that we will
00:04:43;03 calculate later on. One other measure that is intriguing is
00:04:47;28 listed in this spec sheet as the dark current. And the dark
00:04:53;20 current is how much charge accumulates on the chip
00:04:58;19 during a longer exposure when no light is reaching
00:05:03;28 the camera. And so we can simply look that up by setting a longer
00:05:07;24 exposure time. I'll set an exposure time of 5 seconds.
00:05:11;27 Then snap an image. So the dark current is expressed
00:05:17;06 in electrons per pixel per second. And so, now that we have
00:05:25;06 our image here, we see that all of a sudden we start to
00:05:33;18 see these very bright pixels coming out of the black background.
00:05:39;07 So we have what I call "hot pixels." Still, to see if this spec
00:05:46;20 is roughly right, what we can do is measure the standard deviation.
00:05:53;13 And we see that the mean went up by 7/10 or so of a digital number,
00:06:00;04 but you see that the standard deviation went up dramatically.
00:06:03;28 So, the dark current is defined by this mean. So we are
00:06:12;27 1 higher, and if we knew how to convert a digital number
00:06:16;24 into a photoelectron, we could actually check whether this number
00:06:21;22 was about right. And we'll be able to do that later. But the
00:06:25;22 important thing to note is that not all the pixels are accumulating
00:06:30;24 this dark charge the same way. You also see here that
00:06:35;05 in the spec sheet, that the dark current depends on something.
00:06:39;18 And that something is actually the cooling. So the better we
00:06:43;28 cool the camera, and we are now only cooled at -10, if we
00:06:47;21 would cool the camera further, then the dark current would go down
00:06:52;18 and these hot pixels would get less prominent. So we now
00:06:58;20 know how this camera responds when there is no light, and so the next
00:07:03;06 thing is that we want to know how it responds when there is light. One
00:07:07;20 of the things that is difficult to do is to provide a very
00:07:11;04 homogeneous flat source of illumination. And so I used
00:07:16;29 now some very simple tricks to get a relatively even illumination.
00:07:21;08 And I'll show you here at the camera how to do that. The first thing
00:07:25;03 we need to do is take the cap off the camera. So in here,
00:07:29;23 you see the photosensitive chip, the 2048x2048 pixels.
00:07:36;17 And then the other thing I use is these cups that are semi-transparent
00:07:44;25 and kind of act as a diffuser. And those happen to fit very nicely here
00:07:50;09 on the camera. Then, the other concern is the light source.
00:07:56;21 We have fluorescent lights here, those flicker at a 60 hertz
00:08:00;27 rate. That's not very good. And so, it so happens to be that phones
00:08:06;14 provide a much nicer, very continuous light source. So I'm using
00:08:14;19 here a flashlight application on my phone. You also see that it's
00:08:18;25 set to a very dim and low light intensities. And I'll just put this
00:08:22;29 in front of the cups to provide the continuous and relatively
00:08:29;00 even source of illumination. When we snap an image, we
00:08:34;02 see some patterns on it. We also see that it's bright on the top
00:08:40;26 and dark on the bottom. And then when we go live, we notice
00:08:45;26 pretty profound flickering. And that flickering is coming from those
00:08:52;07 fluorescent lights that we still have on in here. So we'll need to
00:08:57;15 switch the lights off to have our constant continuous illumination.
00:09:03;14 With the phone and the cups in front of the camera, snap an
00:09:08;04 image. I see first of all in my histogram that we have bright pixels
00:09:15;08 that are distributed in a relatively narrow area. And what I see on
00:09:20;10 the screen is that we have a relatively homogeneous illumination.
00:09:24;10 Although it's still a little darker here on the corners. And we see
00:09:27;14 some strange folds, we see some strange patterns here.
00:09:32;16 What is highly useful is to again take something like 100 images
00:09:38;07 here, and then average the 100 of them. And so that will then
00:09:45;02 show us how the individual pixels are responding to the
00:09:49;17 light with which we are illuminating. So I acquired 100 images,
00:09:53;26 I then make a projection of it. And what I say is to simply
00:10:03;09 sum all the numbers. And that in the end will give us an
00:10:09;15 average image. And the first thing that we note in that average
00:10:16;00 image is how homogeneous it is. And what we also note
00:10:24;12 that certain pixels respond worse than others. So for instance,
00:10:28;28 right here are some pixels that respond very poorly. Much more
00:10:37;05 poorly than their neighbors. And we also see that there are some
00:10:40;23 patterns that basically are on the photosensitive area itself.
00:10:46;01 One piece of information that is missing and that we really want to know
00:10:50;12 is how these digital numbers correlate with photons hitting the
00:10:55;16 sensor. And so to figure that out, what we're going to do
00:11:01;20 is to take images with illumination like we used here to get that
00:11:06;22 flat field. So homogeneous illumination. And then in those
00:11:11;05 images, we're going to measure the average intensity
00:11:17;00 and we're also going to measure the noise in the image.
00:11:20;28 And so, since the noise is going to be limited, hopefully, only
00:11:28;21 by photon shot noise, we know that that noise should go with
00:11:35;22 the square root of the intensity. And so out of that relation, we can
00:11:40;27 then backtrack what the photon conversion factor is. And
00:11:45;14 I wrote a number of scripts that make it relatively easy and
00:11:52;05 straight forward to measure the photon conversion factor.
00:11:56;25 So what these scripts are going to do is that first, we're going to
00:12:00;23 acquire a data set, and we're going to acquire a data set
00:12:04;07 with increasing exposure times. Every time we're taking
00:12:07;21 two images at the same exposure time, and we're doing that
00:12:12;14 to correct for inhomogeneities in the illumination. Because we take these two
00:12:18;21 images, we subtract them from each other, and from that subtracted
00:12:23;25 image, we calculate the noise. And we correct that then
00:12:28;29 by the square root of two. And so that way, we can actually
00:12:33;25 deal with certain inhomogeneous illumination. So then at the
00:12:41;23 end, we'll have intensities at different intensity levels, and we
00:12:47;27 have the noise, the variants, that we measured from those images.
00:12:53;08 We will plot that on a log-log scale and from that plot, we can
00:12:57;16 deduce the photon conversion factor. So we open the
00:13:02;09 script panel here. I prepared the 3 scripts that we need.
00:13:08;05 We need to run this script "plot" just once. Then we're going to
00:13:17;12 use this script "CameraLabs," and that's what we're using to
00:13:23;23 acquire the data. So we have to enter a few values here, one is
00:13:30;09 the final exposure, 100 milliseconds is okay, 50 exposures is
00:13:36;02 fine. We can start here and 3 milliseconds is also roughly about
00:13:43;21 right. Or we can start at 2.1. And now when I run this,
00:13:53;07 it will be taking images at increasing sets of images at
00:14:00;24 increasing exposure times. These are being autoscaled.
00:14:05;09 So it's only actually from the apparent noise reducing that we
00:14:11;18 see that our exposure times are increasing. Once we have this,
00:14:15;23 we will run the analysis script. And that will now process
00:14:23;17 all the images. And it will give us two things, so one is the
00:14:29;21 photon transfer curve. This is plotting the signal, the mean
00:14:36;00 intensity, as a digital number against a noise, the variance
00:14:41;24 as a digital number. And this is plotted on a log-log plot.
00:14:47;05 And you see that it is relatively straight. Here at the
00:14:53;14 lower end, if we were able to go to very short exposure
00:14:58;22 times, this would go to the readout noise. However, this camera
00:15:05;08 doesn't let us set very short exposure times, so we don't really
00:15:08;29 get that low. There's a little bump here, don't know what that is.
00:15:13;12 You also see that it starts to level off here somewhere at this
00:15:21;01 point. And that is where we are filling the pixels, so we are
00:15:25;08 reaching saturation here. And we can run another one where we
00:15:28;25 go to slightly higher exposure times, and you'll see that it really
00:15:32;21 starts to go down around here. So we have here the photon
00:15:38;08 transfer curve as we measured it. So we see here that
00:15:42;21 it is pretty straight along most of the area where we measured.
00:15:50;05 And we can now in this table, we can look for areas where the slope
00:15:56;29 on the log-log plot is 0.5. And a slope of 0.5 indicates that
00:16:03;22 the relation between the two is the square root, and that means
00:16:09;14 that this is the area that we're really limited by photon
00:16:12;22 shot noise. So wherever that slope is 0.5 or close to it, we
00:16:18;20 can read out the photon conversion factor. You'll see here that the
00:16:23;06 photon conversion factors are in a pretty close area, so roughly
00:16:27;25 between 0.44 and 0.46. So 0.45 is a pretty good estimation for
00:16:33;09 the photon conversion factor. Now, let me go back to the beginning where
00:16:39;06 we measured on a dark image the standard deviation
00:16:43;00 of 3, we now know that we have to multiple that 3 in
00:16:48;20 digital numbers with this 0.45 to get the readout noise
00:16:54;28 in photon electrons. I think the readout noise was actually
00:16:59;15 2.9. And so there, we get a readout noise in photon electrons of
00:17:08;21 1.305. Now when we go back to the spec sheet, we see
00:17:14;23 that the read noise is given as 1.3 electrons root mean square.
00:17:21;27 And so this indicates that we are measuring very much the same
00:17:26;27 thing that the manufacturer measured. And the specs are
00:17:30;22 holding up to what was promised. So the other thing that we are seeing
00:17:35;18 is that we are reaching around here, we are reaching
00:17:39;13 full well capacity. So now our noise is not going up
00:17:43;08 anymore with the square root. And we can read out
00:17:47;29 here that it is happening around a signal in digital numbers
00:17:56;20 of about let's say 55,000. And so this indicates that we are reaching
00:18:03;26 full well capacity. And likewise, we can now multiply
00:18:09;08 55,000 by our photon conversion factor of 0.45, and from that we get
00:18:17;17 a full well capacity of roughly 25,000. Now the manufacturer
00:18:24;08 gives a full well capacity of 30,000. One thing that is possible
00:18:28;28 is that we are here not reaching the real full well capacity
00:18:33;20 of the pixels itself, but we're getting close to 64,000,
00:18:40;15 which is the end of the 16-bit range. So we're just starting
00:18:45;09 to cut off pixel values, and that will also reduce the actual noise here.
00:18:51;01 Okay, I hope I explained to you how with very simple means,
00:18:55;00 you can check the quality of your camera. And you can really
00:19:01;26 quite easily measure if your camera is performing the way you
00:19:05;23 would like it to perform.

This Talk
Speaker: Nico Stuurman
Audience:
  • Researcher
Recorded: April 2012
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Talk Overview

In this video about camera calibration, Nico Stuurman shows you how to measure a camera dark image, calculate the readout noise, estimate the dark current, get a camera flat field image using a plastic cup and a cell phone screen, and estimate the photon conversion factor and full well capacity by measuring a photon transfer curve.

Speaker Bio

Nico Stuurman

Nico Stuurman

Nico Stuurman is a Research Specialist at the University of California, San Francisco, in the lab of Ron Vale. Nico combines his expertise in computer programming and microscopy to advance many projects including the Open Source software, Micro-Manager. Continue Reading

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