Characterizing Your Cookbook CCD Camera
The "vital statistics" that define the performance of a CCD camera can be measured from test images. These characteristics include the conversion factor, the read-out noise, the linearity, and the uniformity of the CCD. In addition, the CCD can be checked for bit bias, noise pickup, and charge trapping from the same test images. The information gained is used to verify that a CCD camera is operating correctly. The Cookbook 245 CCD camera and Check245 software serve as examples here, but the methods described and the test logic are valid for all CCD cameras.
This document is too long (~50k) to read on the screen of your browser. We suggest that you print a copy for later study. To skim this document, click on the topic headings listed. Click below if you want to download the Check245 software. This is the second version of this text posted, and includes tables missing from the initial posting.
The primary goals of characterizing and checking are to verify the correct operation of a CCD camera and to verify its stability over time. Should a problem be discovered, it can be corrected.
The conversion factor, sometimes called the gain, ties the arbitrary unit of pixel value (or "analog-to-digital unit") found in images to the physically meaningful number of electrons generated by photosites on the CCD. Furthermore, measuring the conversion factor enables you to characterize other aspects of the performance of the CCD, such as the dark current, in the physically significant unit of electrons. If testing shows that the conversion factor is not optimum in your camera, the gain of the amplifier circuit can be changed to an optimum value.
Read-out noise is the irreducible "bottom line" for noise in a CCD chip, the random variation in the output of the CCD when no signal electrons are present. It is customarily expressed at the root-mean-square variation in number of electrons detected by the CCD. Determining the read-out noise allows the performance of a given CCD to be compared with the manufacturer's specifications and with other CCDs. If the measured read-out noise is "below spec," this test should alert the user to locate and correct this problem in the CCD camera's performance.
Read-out noise is intrinsic to the CCD, but noise from a variety of other sources is not. Noise can be picked up from a variety of sources in and around the telescope. If noise is found in the test set, its characteristics can be used to identify the source so that the noise can be reduced or eliminated.
This test verifies the proper functioning of the analog-to- digital converter and its related circuitry. If one of the high- value bits in the digitized signal is "stuck," then the pixel values in the image will obviously be in error. However, if one of the low-value bits is stuck, the problem may not be evident without bit-bias checking.
When an image is clocked out, in some CCDs photosites that contain defects or impurities may trap (or "skim") and release signal electrons as they pass through it. Since the skim charge is typically less than 100 electrons, the effect is troublesome only when signal levels are quite low. The Texas Instruments CCDs used in the Cookbook cameras do not normally show charge skimming. The purpose of this check is to verify the absence of traps and charge skimming.
Ideally, the pixel value is directly proportional to the light that has fallen on the CCD. When this is the case, images from the camera can be precisely flat-fielded and used for precise astrometric and photometric measurements. As the charge wells on the CCD approach saturation, for example, the CCD may become nonlinear. Charge skimming is a nonlinear response at low light levels. The goal of this test is to verify the linearity of the CCD over its full dynamic range, or to determine the range over which the CCD is linear so that the amplifier gain can be optimized.
The accumulated charge from thermally generated electrons grows linearly with time. Electrons are generated in the neutral bulk silicon, in the charge depletion region, and in surface states at the interface between the bulk silicon and the silicon dioxide insulation layer. Cooling the CCD reduces the rates at which thermal electrons are generated. In the Cookbook CCD cameras, dark current can be reduced significantly by operating the CCD with the bias inverted (i.e., in low-dark-current mode), which reduces the contribution from surface states, but also reduces the full-well capacity. The goal of this test is to verify the correct operation of low-dark-current mode and to measure the dark current in physical units (electrons per second per pixel) for comparison with the manufacturer's specifications and with other CCDs.
The photosites on the CCD vary in their sensitivity to light. Between adjacent pixels the variations are typically less than 1%, but the variation may reach 10% across the entire CCD. Characterizing its uniformity establishes that the CCD is operating within normal boundaries.
To be practical for most amateur astronomers, a CCD testing must be simple enough to be carried out without complex auxiliary equipment. The test sequence described below requires only the CCD camera system, a location that can be made dark, and a stable, low-level light source. The following section describes a low-level light source that is inexpensive, portable, and easy to construct. A complete set of test images consists of shooting nine bias frames, nine low-level flat-field frames, 32 flat-frames at different integration times, and three long-integration dark frames. The test sequence can be done indoors, in an amateur astronomer's observatory, or as noted above, in any place that can be darkened. Obtaining a set of test images takes about three hours.
The purpose of the low-level light source (L3S) is to provide a stable, uniform source of illumination for exposing the flat-field frames needed for the test sequence. The apparatus described here is simple to construct, reasonably robust, and adequate for testing CCDs used for amateur astronomy.
The standard L3S is a plywood box 6 inches square and 24 inches long as shown in the accompanying diagram. At one end a bulkhead isolates the light source and holds a diffusing screen. In front of the diffusing screen is a holder that can accept slides with different size holes (apertures) drilled in them. The center of the box is empty except for two baffles to reduce scattered light. At the far end is another bulkhead with a holder that accepts an opaque dark slide, another diffusing screen, and the CCD camera. By changing lamps and apertures, the illumination reaching the CCD from the L3S can be changed by a factor of roughly one million in brightness.
The light source can be a standard 120 VAC household electric light bulb, a low-voltage tungsten halogen lamp, or a brightness-stabilized LED depending on the importance of insuring precise linearity in the CCD. An L3S using a 120 VAC light bulb is by far the easiest type to construct, and is adequate for testing CCDs used for imaging. Tungsten lamps gradually darken when they run, and of course their light output varies if the line voltage varies. The tungsten-halogen option is less prone to lamp aging effects, but less easy to construct. A brightness- stabilized LED option is most stable light source, but the builder must be prepared to run auxiliary tests to check for proper functioning of the LED stabilization circuit. A stabilized LED might be required to verify the linearity of a CCD used for precision photometry, but is not necessary for most other CCD applications. For the tungsten lamp option, a 120-volt 15-watt appliance lamp is a good starting point. These lamps are rugged and designed to have a long life.
The lamp section. The rear six inches of the L3S unit houses the light source, and is sealed by a rear bulkhead and the "aperture" bulkhead on which the aperture slide is mounted. If the lamp is rated larger than 15 watts, drill holes in the rear bulkhead so that the lamp chamber stays cool. The aperture bulkhead of the lamp area must not leak light in the direction of the CCD.
The amount of light that reaches the CCD depends on the construction of the individual L3S, so construct the lamp section so the lamp can be placed close to and directly behind the diffusing screen, further back, or positioned to the side and shielded so that a reduced amount of light reaches the diffusing screen.
The diffusion screen. The diffusion screen is a piece of opal glass or milk plastic roughly two inches on a side. Opal glass and milk plastic are both translucent materials that completely scatter incident light. Both materials look like whole milk, that is, they appear smooth and uniformly white.
The slide holder and aperture slides. The slide holder is mounted on the aperture bulkhead so that slides can be inserted from the top of the L3S. It can be constructed from stiff cardboard or thin wood, and should be painted black to minimize light leakage. The aperture slides themselves are thin pieces of cardboard or wood two inches wide by six inches long, and roughly one inch from the bottom end is a recessed area to which is glued a thin sheet of metal with a hole drilled in it. For maximum versatility, make eleven slides and in each place metal sheets with one or two holes drilled in it. The largest hole (aperture A1) should be 1 inch diameter and the smallest (aperture A11) should be 1/32 inch diameter. The intermediate slides should have two 1/2-inch holes, one 1/2-inch hole, two 1/4-inch holes, one 1/4-inch hole, two 1/8-inch holes, one 1/8-inch hole, two 1/16- inches holes, one 1/16-inch hole, two 1/32-inch holes, and finally the smallest with one 1/32-inch hole. Made in this way, each slide passes approximately half the light of the one before it in the series.
The middle of the L3S box. Between the aperture bulkhead and the dark-slide bulkhead are two baffles to reduce scattered light. Each baffle has a hole approximately two inches diameter in the center, and the surfaces should be blackened. In the standard design, the distance between the aperture bulkhead and the dark slide bulkhead is approximately 12 inches.
The dark-slide bulkhead. Mounted on the dark-slide bulkhead is a slide holder identical to the aperture slide holder with an opaque slide, and behind it is a second diffusing screen. On the other side of the bulkhead is a holder that accepts the CCD camera. The separation between the diffusing screen and the CCD should be kept as small as practical to insure even and shadow- free illumination of the CCD chip. The bulkhead should be set into the box by the depth of the CCD camera so that the camera can be isolated in a dark and thermally stable environment.
Because it is often necessary to experiment to find a lamp of the right brightness, construct the box with a removable top. In use, the box is draped with black cloths to keep the camera in total darkness. Mark the aperture slides and the dark slide for easy identification under low light.
Assemble the unit with glue and screws. Carefully seal all light leaks around the aperture bulkhead and slide holders. Using strong light from behind, check that no light sneaks around the edge of the aperture slide and the dark slide.
When you turn on the lamp with the largest aperture in place and the dark slide pulled out, you should be able to see a small amount of light on the second diffusing screen. Placing the lamp in the L3S and determining its wattage requires measuring the signal generated by your CCD camera.
The standard scheme described above works well. However, it is not necessary to adhere rigidly to the dimensions and materials described. Any method of providing adjustable, low- level diffuse illumination to the CCD will serve for testing the CCD.
For testing the Cookbook 245 CCD camera, a program called Check245 (written and distributed by Richard Berry) carries out the specialized image processing tasks needed to analyze sets of test images. Check245 runs under DOS or in a DOS window under Windows 3.x or Windows 95. It includes the following functions:
Check245 produces accurate and meaningful results when it is used with image data that has been obtained properly, and only when the functions are applied in the proper way. As noted above, values displayed on the screen are meaningful only in the proper context. The user accepts full responsibility for obtaining valid image data, properly applying the functions in Check245, and interpreting the program's output.
Setting the brightness of a newly built L3S will take several iterations. The goal is to place the lamp behind the first diffusing screen at a distance such that when the CCD is attached to the L3S, it generates a signal 100 pv above the bias level in a 10-second integration using aperture A5 (one 1/4-inch opening). This amount of light means that the L3D can generate the brightest and faintest levels needed in subsequent testing. To put the light levels generated by the L3S in context, under a fairly dark rural sky on an f/5 optical system, the standard Cookbook 245 camera in 378-wide mode produces a sky background signal of roughly 1.5 pv per second, which is the same signal level that the L3S generates with aperture A9.
Install the CCD in the L3S. Swaddle the end of the box with CCD in black cloth, then turn on the camera's electronics and cooling system and allow the CCD to reach equilibrium--at least 15 minutes. Use the read-out mode that you most often use to make celestial images. With the aperture A5 in place and the dark slide closed, make an integration of 100 seconds and save it as a dark frame, then open the dark slide and make a second integration of 100 seconds and save it as a bright frame.
Using Check245 software, load the light frame (LO) and then subtract (SU) the dark frame from it. With the Measure Noise (MN) function, determine average pv of a region near the center of the frame. Repeat the process of making and measuring images, altering the position of the lamp in the L3S as necessary, until the signal is close to 1000. It need not be exact: any value between 800 and 1200 pv is close enough. With the light output from the L3S set, you are ready to begin testing.
The purpose of making initial test images is to get a quick and dirty estimates of the conversion factor and read-out noise of the CCD camera. This is not an accurate determination, but it helps to have some "ball park" figures before you start the more thorough test run.
Once again install the CCD in the L3S. Swaddle the end of the box with CCD in black cloth, then turn on the camera's electronics and cooling system and allow the CCD to reach equilibrium--at least 15 minutes. Use the read-out mode that you most often use to make celestial images.
With the brightness range of the L3S set, take the following images:
To make the bias frame, close the dark slide, set the integration time to zero (0.001 seconds is close enough), then make the integration and save it.
For the two flats, open the dark slide, and then make and save two integrations. Since you have adjusted aperture A5 to produce a signal of approximately 10 pv per second, a 100 second integration should produce the desired signal level of 1000 pv. Because each aperture step represents a factor of two in brightness, the integration time necessary to produce a signal of 1000 pv with aperture A4 would be 50 seconds, while the integration time with A6 would be 200 seconds, with A7 400 seconds, and so on.
To make the dark frame, close the dark slide, and then make an image with the same integration time you used for the flats, and save it.
Using Check245 software, load the bias frame. Using the measure noise function, determine the standard deviation of the pixel value for the default region near the center of the frame. This quantity is sigmapv. Since the only noise present in the bias frame should be read-out noise, this is a direct measurement of the read-out noise in the bias frame in pv units.
Next, load one of the flats and then subtract the dark frame from it. With the measure noise function, determine the average pv of the default region near the center of the frame. This quantity is Spv, and if you have set the L3S properly, its value should be close to 1000.
Next load one of the flats and subtract the other using the merge function. Multiply the first frame by 1, the second frame by -1, and add a constant of 1000. Then using the measure noise function, determine the variance. This quantity is sigmapv2. Because you have combined noise from two flats, the variance is twice the variance of a single image, which explains the factor of 2 in the equation below.
From the measured quantities, evaluate the following:
For the conversion factor: g = 2 * Spv / sigmapv2 e-/pv
For the read-out noise: re = g * sigmapv e-
The values you obtain should be rough accord with the accepted values for the appropriate operating mode of your camera. The quick assessment should help you in making test images with the desired signal levels.
The following table shows a set of preliminary test data:
| Frame | Spv
(mean pixel value) |
sigmapv
(standard deviation) |
sigmapv2
(variance) |
Notes | |
| Bias |
0.761 |
||||
| flat1-dark |
1476.1 |
||||
| flat1-flat2 |
108.91 |
||||
| Results: | g = 27.1 e-/pv | re = 20.8 e- |
Make the test images after the CCD has been running long enough to reach thermal equilibrium. If in doubt, allow the camera to equilibrate for 60 minutes in the L3S. The purpose of waiting this long is to minimize temperature changes during the test run. For your initial tests, use the read-out mode that you most often use to make celestial images. You may later wish to test your camera in each of its read-out modes.
To look for noise in the read-out system of the CCD camera, you need to read out the CCD with no light falling on the CCD and zero integration time, so that the only signals are the zero- point offset (i.e., the bias), read-out noise from the CCD's amplifier, and any electronic interference present. For the Cookbook 245, a dark frame taken with an integration time of 0.001 seconds works very well as a bias frame.
These frames will be saved as BIAS001 through BIAS009.
To detect traps in the CCD, you need to make low-level flat frames. The total charge that accumulates during integration should total less than 300 electrons and the integration should be sufficiently short that hot pixels do not exceed this value. With a standard Cookbook 245, an integration time of 5 seconds with aperture A9 should produce the desired number of signal electrons.
These frames will be saved as SKIML001 through SKIML009 and SKIMD001 through SKIMD009.
To determine the conversion factor (electrons per pv) and test the linearity of the CCD, take a series of flat frames of increasing exposure. Because the lamp in the L3S may vary in brightness, divide the flats into a set with increasing integration times and a second set with decreasing integration times. With a standard Cookbook 245, integration times from 1 second to 100 seconds with aperture A5 should span the desired range. In the steps below, "xx" designates the integration time.
Remember that you are taking three frames for each integration time--two flats and one dark. It is easy to become confused when carrying out these rather boring and repetitive operations, so stay alert.
To determine the dark current of the CCD, take a set of dark frames with an integration time long enough to produce dark current in all pixels, but short enough that none of the pixels saturates. If the cooling system is operating properly, an integration time of 500 seconds will satisfy these requirements.
Probably the most important thing to bear in mind as you analyze the test image sets is to really look at the images and the plots made from them. But carry out your examination with an eye that is both analytical and quantitative. Noise that looks like a mountain range on one graph may have an amplitude of 0.05 pv and prove insignificant, while a small bump in a Fourier Transform plot may be the diagnostic clue needed to find to an insidious noise source with an amplitude of 1.2 pv. At all times, keep in mind your ultimate goal of making astronomical images.
Load and examine each of the bias frames by eye using the inspect function. Use the [del], [ins], [home], and [end] keys to apply the scaling that most strongly accentuates the noise and interference present. After inspecting each bias frame, use the measure noise function to determine the average pixel value, Spv, and the standard deviation of the pixel values, sigmapv, in the bias frame. Finally, check the lines and columns for noise pickup and interference using the line analysis and column analysis functions.
The ideal bias image consists of an unvarying bias plus read-out noise; that is, the values of the pixels in the frame should vary about an average value (the bias value) with a Gaussian distribution. The standard deviation of the variation is the read-out noise. In the preliminary assessment, you calculated the read-out noise in units of equivalent number of electrons variation.
However, a typical "real world" bias frame will show variations from top to bottom and left to right, patterns of various kinds, as well as random and pseudo-random variations in the intensity of the lines and columns. In each frame, check for the following:
After you examine each of the bias frames, use the create median function to make a median bias frame. (If you have not already converted all your images to the FITS format, use the convert-to-FITS function to convert the images to files with the extension .FIT.) To create a median bias frame, you must supply a name (BIAS-MED.FTS) and a selection mask (BIAS*.FIT). The function will automatically create median stack.
Scrutinize the median bias in the same way you did each of the individual frames. Features of the bias frame that remain the same from frame to frame will be present in the median bias, and features that change will be absent. This is one of the best ways to determine whether a noise source is coherent (related to the camera's frame-taking process) or incoherent and therefore probably external to the camera system.
Next, using the measure noise function, determine the average pixel value and the standard deviation, sigma, for each of the bias frames. The average bias value should vary by no more than 1 pixel value from one frame to the next. Write these values in the bias frame report. Here are some sample values from a set of bias frames taken in 252-wide internal binning mode:
| Frame | Spv | min pv | max pv | sigmapv | Notes |
| Bias001 | 100.21 | 99 | 102 | .761 | |
| Bias002 | 100.17 | 99 | 102 | .779 | |
| Bias003 | 100.24 | 99 | 102 | .773 | |
| Average | 100.21 | .771 pv |
Finally, examine each frame using the line analysis and column analysis functions. These two functions do two things: they find the averages of the lines and columns and they find the average Fourier transforms of the lines and columns.
Each of these functions first finds the average value of all the lines or columns in the image and displays the result in a graph with the maximum and minimum values. This analysis is very sensitive to coherent noise sources. Slopes and other features stand out clear in this graph even if they are hard to see on the bias frames themselves. Note the amplitudes and the degree of repeatability.
Next, each of these functions determines the average Fourier transform of each line or column. This analysis is quite sensitive to incoherent noise sources that have a well-defined frequency that is not necessarily in synchronization with the CCD's frame read-out timing. Power supply ripple, switching transients, and interference from nearby electronic devices produce peaks in the graph of the Fourier transform. The maximum and minimum values of the graph and the amplitude of the zero- order Fourier term allow semi-quantitative comparison of the CCD's performance with itself and with other CCDs.
If you are not familiar with Fourier transforms and their use, look at the graphs but ignore them. Most of the things they can reveal are evident from a careful visual inspection of bias frames. If you are familiar with Fourier theory, the analysis routine takes the FFT of the nearest power-of-two less than the line or column length. The resulting transform is scaled to graph the first through n/2-th component of the spectrum, and the values of the maximum and minimum values displayed, as well as the value of the zero-order peak. The highest frequency displayed in the line analysis routine therefore corresponds to the half the pixel read-out frequency, or 33.3 kHz for 252-wide internal sampling, 11.1 kHz for 252-wide external sampling, and 16.7 kHz for 378-wide external sampling. In column analysis, the highest frequency displayed half the line read-out frequency, or 133 Hz for 252-wide internal read-out mode, and 44 Hz for the 252-wide external and 378-wide external read-out modes. If it is present, 60 Hz interference will show up as a strong peak near the middle of the column analysis Fourier spectrum of 252-wide internal bias frames.
The outstanding characteristic of a good bias frame is its blandness. The pixel value is nearly constant across the frame and the random variation of the pixel values should itself be very bland. Coherent noise features less than 1 pixel value in amplitude are seldom cause for concern since they are subtracted during routine image calibration. If at all possible, incoherent noise sources should be identified and removed.
Charge skimming occurs when an abnormal photosite retains a few hundred electrons during read-out. The characteristic signature of charge skimming is a dark pixel at the location of the charge "trap" and a dark tail of pixels following the trap.
Because the signal levels are so low in this check, it is necessary to shoot a fairly large number of frames and combine them to reduce the noise level. Furthermore, because of the hot pixels present even in short-integration flat fields, it is necessary to make and subtract a dark frame to remove the hot pixels.
To check for charge skimming, make a median stack of the nine skim dark frames using the create median function. Name this frame SKIMDMED.FTS. Make another median stack of the skim frames, and name this frame SKIMLMED.FTS. Use the merge function to subtract SKIMDMED from SKIMLMED, and add an offset of 100. Examine this image carefully for dark pixels and their associated tails.
Because TC245 CCD chips seldom exhibit charge skimming or traps, you may decide to treat this test as optional.
The transfer curve is a graph of the variance, sigmapv2, against the average pixel value, Spv, for a set of flat-field images. The variance at different levels of pixel value is found by subtracting the pairs of flat-field frames. The transfer curve and the test for linearity use the same set of measurements from the flat-field data-- Check245 reduces and displays the same data differently. From the transfer curve, you can determine the conversion factor of your CCD in electrons per pixel value and the read-out noise of the CCD.
Reducing the transfer relies on the counting statistics of events such as the generation of photoelectrons to have a Poisson distribution; that is, the standard deviation (sigmap) in the number of photoelectrons received in each sampling interval equals the square root of the average number of photoelectrons, Sp. If on the average, the light falling on a given photosite generates 10,000 photoelectrons per integration period, then the standard deviation will be sqrt(10,000), and the number of photoelectrons expected in any given sampling period will be 10,000 +/- sqrt(10,000) electrons.
In a healthy CCD, the signal consists of a combination of noise from Poisson counting statistics and the read-out noise of the CCD. Since standard deviations add quadratically, we expect the standard deviation of the combined signal, sigmae, in units of equivalent electrons at the detection node, to be
sigmae = sqrt(sigmap2 + sigmaron2),
where sigmap is the standard deviation in the number of photoelectrons and sigmaron is the read-out noise expressed in electrons.
For each of the flat-field images, we can directly measure the average pixel value, Spv, from images in units of pixel value. This is equal to the total number of photoelectrons at the detection node, Se, times the conversion factor for the number of electrons per pixel value unit, g:
Se = g * S
For the photoelectron component of the electrons reaching the charge detection node, the standard deviation, sigmap, equals sqrt(Sp), so the variance, sigmap2, equals Sp. Thus, by substitution,
sigmap2 = g * Spv.
Another quantity we can measure is the standard deviation of pixel values in a flat-field frame, sigmapv. Even though flat- fields are never perfectly "flat", by subtracting one flat-field image from another flat-field image made under identical conditions we can eliminate all of their nonuniformities and determine quadratic sum of the noise. The noise measured in electrons is scaled by the conversion factor into pixel value units,
sigmae = g * sigmapv.
Note that the measured variance using this technique is twice the variance of a single flat-field frame. When you record data from these images, DO NOT divide the variance. Check245 performs the necessary division for you.
Substituting the above equalities into the equation for the noise in an image,
sigmae2 = sigmapv2 + sigmaron2,
we obtain
g2 * sigmapv2 = g * Spv + sigmaron2
which can be rewritten
sigmapv2 = Spv/g + sigmaron2/g2.
This is a linear equation in the form y = mx+b. You can measure sigmapv2 and Spv directly from the images in pixel value units. Graphing the variance of the signal against the signal itself, we expect a straight line plot. The inverse of the conversion factor, 1/g, is the slope of the line and the square root of the intercept on the y axis is the read-out noise in electrons.
To derive the transfer curve, load the first flat-field frame in each integration-time set, subtract the dark frame, and then measure the average illumination of the frame in pixel values using the measure noise function. Next, load the first flat-field frame again but this time use the merge function with a coefficient of 1 for the first frame, -1 for the second frame, and add a constant of 1000 to keep all values positive. Use the measure noise function to determine the variance, sigmapv2. Copy these values for each pair of flat-field frames into a table.
The transfer curve function can perform a least-squares fit of this data and solve for the conversion factor and read-out noise. Start by entering the measurements you have made using the type data function. Enter each set of values. (Note that Check245 expects the variance that you actually measured, so do not divide the variance figure.) Once the data has been entered, run the transfer curve function to perform the analysis. This function displays a plot of the transfer curve.
Here is a sample set of data taken in 378-wide LDC mode:
| Flat set | Integration
(seconds) |
Spv
(mean pv) |
sigmapv2
(variance) |
Notes |
| Flat01 | 1 sec | 59.2 | 2.98 | increasing |
| Flat03 | 3 sec | 171.2 | 7.36 | |
| Flat05 | 5 sec | 284.1 | 11.16 | |
| Flat09 | 9 sec | 469.8 | 19.05 | |
| Flat15 | 15 sec | 769.8 | 31.05 | |
| Flat25 | 25 sec | 1377.3 | 49.78 | |
| Flat45 | 45 sec | 2417.4 | 83.14 | |
| Flat35 | 35 sec | 1865.9 | 65.67 | decreasing |
| Flat20 | 20 sec | 1101.8 | 41.33 | |
| Flat12 | 12 sec | 685.1 | 26.26 | |
| Flat06 | 6 sec | 340.0 | 13.46 | |
| Flat04 | 4 sec | 224.1 | 9.40 | |
| Flat02 | 2 sec | 112.2 | 5.25 | |
| Flatp5 | 0.5 sec | 24.3 | 1.86 |
Although it is possible to compute the read-out noise from the transfer curve, it is more reliable to convert the standard deviation of the bias frame to electron units.
In the Cookbook 245 camera, the conversion factor and read-out noise are different for each read-out mode because each mode employs a different scheme for binning and summing the charge packets from the chip. In the basic 252-wide internally binned mode, charge packets from three photosites are clocked into the detection node and read out once; the nominal conversion factor is 34.4 e-/pv and the read-out noise is 30 e-. In 252-wide externally binned mode, charge packets from three photosites are clocked into the detection node and read separately, then summed and divided by four in the computer; the resulting conversion factor is 54.8 e-/pv and the read-out noise is sqrt(3) * 34.4 = 54.8 e-. In 378-wide externally binned mode, charge packets from two photosites are clocked into the detection node and read separately, then averaged in the computer; the resulting conversion factor is 56.6 e-/pv and the read-out noise is sqrt(2) * 34.4 = 44.7 e-.
Your measurements may vary from the nominal values because the gain of the one-chip amplifier and the following electronics may be different, and your read-out noise may be markedly lower than expected because the read-out rate of the Cookbook camera is 67 kilopixels per second versus the nominal 4.77 megapixels per second that Texas Instruments specifies for the TC245.
Check245 verifies the linearity of the CCD by computing and comparing the rate at which the pixel value increases for different integration times. In a camera that is linear, the count rate is the same for all integration times.
Since you have already made the necessary measurements and entered them into the Check245.dat file to derive the transfer curve, start the linearity curve function. You will see a table in which the count rate is displayed in pixel values per second. The spread around the average value should be small.
The linearity curve function also graphs the count rate values. If the count rate is constant, the individual count rates will cluster around a straight horizontal line. If the CCD is nonlinear at high values because it is operating near saturation, the values will drop. If the the lamp in the L3S changes in brightness while you were taking the flat fields, the count rates taken while you were increasing the integration time will not overlap the count rates taken during the decreasing integration times. Nonetheless, the average position of the two curves should be horizontal.
If the CCD becomes nonlinear at average pixel values less than 4095, determine the highest pixel value for which the CCD is linear. You may wish to increase the gain of the amplifier by increasing the value of resistor R43 by the ratio of 4095 over the maximum linear pixel value to make the camera becomes linear over the entire range of pixel values.
The charge stored on the biased capacitors of the CCD's photosites decays with time. Cooling the CCD and changing the bias on the device strongly affect the magnitude of the dark current responsible for bleeding off the charge. Although this test is directed to measuring the dark current under normal operating conditions, it can also be applied to measuring the optimum bias during integration.
In the Cookbook cameras, the dark current depends strongly on the bias applied to the antiblooming gate during integration. When the CCD is run in low-dark-current (LDC) mode, the dark current at most photosites drops by a factor of roughly 100, but a residual population of photosites with surface-state defects continue to generates nearly the same dark current even when LDC mode is active. Thus in LDC mode, the most active photosites may show 1,000 times greater dark current than the most common value seen for photosites on the CCD. This population of hot pixels greatly increases the average dark current.
To characterize the wide range of dark currents from the CCD, the Check245 analysis determines both the average dark current and the dark current seen from the greatest number of pixels. In addition, Check245 computes the dark current from the 99th percentile of pixels, and of the hundredth hottest pixel, the tenth hottest pixel, and the "hottest" pixel in units of electrons per pixel per second.
Because the dark current is so low in LDC mode that it approaches the bias level, it is crucial that you make a bias frame immediately after taking the last of the long-integration dark frames.
To determine the dark current statistics, load dark frame DARK003 and merge the bias frame BIASDARK frame using the parameters 1, -1, and 100, then apply the dark current function. You will need to supply the bias level in the resulting image (100), the conversion factor that you have previously determined, and the integration time for the dark frame. If you wish to measure the dark current from images taken with drift subtract on but without a fresh bias frame, use the nominal bias value of 100--but remember that a small error in the bias value results in large errors in the dark current calculated for the photosites with the lowest dark currents.
As a cross-check on the validity of your data, the dark current produced by the "hottest" photosites should turn out the be the same regardless of the imaging mode. This is because the current from the surface state defect that causes the hot pixel remains the same even regardless of how the photosite is binned.
The Cookbook 245 running on a water-cooled Peltier module with LDC ON should have an average dark current in the vicinity of 1 electron per pixel per second. The hottest pixels will have dark currents of roughly 200 electrons per pixel per second, and the most common dark current is one electron per pixel per second.
Load a well-exposed flat-field image. Use the bit bias function to compile statistics on the frequency of 1's for each image bit. The low-value bits should all have values close to 0.5. At some level, typically around the seventh or eighth bit, the statistics will diverge strongly--you should expect bit frequency values from nearly zero to nearly one. This is normal because bit patterns near those of the average pixel value are the most frequent.
If you notice strong departures from bit frequencies of 0.5 among the first five or six bits, load other flat fields or better yet, load images having a wide range of pixel values, and check whether you see one or more bits consistently low or high. A consistent departure from 0.5000 indicates a "sticky bit" in the analog to digital converter chip; a pattern in which one bit is always 0 or always 1 indicates a "stuck bit" probably due to a fault in the camera's digital multiplexing logic.
Load a flat-field image with at least 2000 pv and subtract the appropriate dark frame. Use the inspect function to examine it closely. Despite all of your efforts to illuminate the CCD uniformly, you will almost certainly see considerable structure in the flat-field image. This probably originates from variations in the silicon boule from which your chip was made. Note the low and high scaling values; these typically differ by less than 5%.
Carefully examine the values of adjacent pixels. In the TC245, a small-scale horizontal patterning two to four pixels long with an amplitude of two or three pv is not uncommon; it is probably due to minute errors in the spacing of the column on the CCD.
You can also use the column and line analysis functions to check the amplitude of large-scale sensitivity variations across the chip and to look for the distinctive signatures of small- scale patterning in the Fourier spectra of the lines and columns. Normally you will detect nothing more than problems with small amplitudes.
If you wish to examine the uniformity of the CCD with more precision, shoot a large set of identical flat-field frames and flat-dark frames. Use the create median function to make a single flat-field image with very low noises, and examine it for structures. Normally, unless the intrinsic nonuniformities in the CCD exceed 10% across the chip and 1% over short distances, standard flat-fielding procedures will entirely remove the effects of these nonuniformities from your images.
According to Texas Instruments specifications, the TC245 generates an output of 4uV per electron, has a full-well capacity of 80,000 electrons, and shows an equivalent read-out noise of 30 electrons. The standard Cookbook 245 is designed to produce images with the largest dynamic range possible from this CCD.
The amplification stages in the standard Cookbook 245 have a gain set by the ratio -R43/R45, which is -39 kohms / 2.2 kohms, or -17.7. (The negative value means that the amplifier inverts the signal.) This makes the signal reaching the ADC 70.9uV per electron, so the full-well signal of 80,000 e- from one unbinned photosite generates 5.67 volts at the ADC, or 2324 analog-to- digital units. The conversion factor is therefore 80,000 e- in 2324 counts from the analog to digital converter, or 34.4 e-/pv. Note that the full-well capacity of the serial register and charge node are considerably greater than that of a single photosites, and that these binning strategies are used to extend the dynamic range of the camera.
When you make an image, the Cookbook 245 bins either three three photosites (252-wide modes) or two photosites to generate each pixel in the image. The binning technique and subsequent math operations in the computer determine the effective conversion factor and read-out noise for the pixels in your images.
In 252-wide internal binning, charge from three photosites are clocked into the read-out node and converted in a single read. For 252-wide internal binning, the conversion factor is nominally 34.4 e-/pv and the read-out noise nominally 30 e-. This mode has the lowest noise and is therefore most useful for observations that require high sensitivity.
In 252-wide external binning, the serial register is clocked and read three times for each pixel, and the resulting values are summed and divided by four, which raises the conversion factor by a factor of four. Combining three reads increases the read-out noise by a factor of sqrt(3). The conversion factor is nominally 137.6 e-/pv and the read-out noise nominally 51.9 e-. This mode has a long dynamic range.
In 378-wide external binning, the serial register is clocked and read twice times for each pixel, and the resulting values are summed and divided by two, raising the conversion factor by a factor of two. Combining two reads increases the read-out noise by a factor of sqrt(2). The conversion factor is nominally 68.8 e-/pv and the read-out noise nominally 41.4 e-. This mode has the smallest equivalent pixels and the highest resolution.
The nominal performance of the Cookbook 245 is summarized in the table below. (Note that the readout noise values include digitization noise, so the figures are slight larger than those given in the discussion above.) The conversion factor can be changed by changing the value of resistor R43. Because the read-out in the Cookbook 245 is slower than the design values, the nominal readout noise in a properly constructed Cookbook camera should be regarded as the upper limit of acceptable noise.
| Parameter | 252W INT | 252W EXT | 378 W EXT |
| Binning | 3 pixels | 3 pixels | 2 pixels |
| Conversion | 34.4 e-/pv | 137.6 e-/pv | 68.8 e-/pv |
| Readout Noise, e- | 31.6 e- | 54.8 e- | 44.7 e- |
| Readout Noise, pv | 0.92 pv | 0.40 pv | 0.60 pv |
Three cameras for which we have data show lower readout noise than the nominal values. For three different cameras, readout noise values were 20.8, 25.0, and 23.4 e- in 252-wide internal binning mode. Dark currents for the cameras were 1.4, 1.5, and 1.0 e-/pixel/sec respectively with LDC mode turned on.
The author wishes to thank Rafael Gonzalez and Michael Gutzwiller for stimulating his interest in measuring noise in the Cookbook camera, and Veikko Kanto, David Groski, Steve Lee, Greg Bothun, Mark Nelson, Taner Dosluoglu, Armin Rest, Timothy Abbott, and the faculty of Steve Howell's CCD School (held at the University of Arizona in 1991) for their inputs, ideas, and insights.
Check245.EXE runs under DOS or in a DOS window under Win 3.x or Windows 95. No support for this software is provided beyond this documentation. Click here to download Check245.EXE.to your computer via FTP. The executable is ZIP'ped into a file 85kbytes in size.
Return to the Cookbook Home Page