Software: CCDsoft.

Web Reference: http://www.apogee-ccd.com/ccdu.html

References: Buil, Christian. 1991, CCD Astronomy, (Willmann-Bell, Inc., Richmond, Va.).

The term "CCD" means Charge-Coupled Device. The CCD is a solid state sensor consisting of a wafer of silicon crystal. When the silicon wafer is exposed to light, the photoelectric effect liberates electrons from the silicon bonds. These free electrons are collected and deposited in potential wells in the silicon wafer. When the exposure is completed, the potential wells are "emptied" into a register. The computer counts the number of electrons liberated from each pixel (small square area) of the silicon wafer. The number of electrons liberated is proportional to the number of photons that entered the pixel during the exposure.

Even though CCD cameras and chips are mass-manufactured, every CCD camera is unique. While the manufacturer is able to indicate ranges in which your CCD camera's operation will fall, it is always wise to check the camera yourself, to find out the exact response of your camera over the entire range of possible conditions. The procedures described in this lab can be carried out before or after the installation of the camera on the telescope. In some cases, a slight modification may be required, but both situations are covered here.

The typical CCD sensor responds differently to different wavelengths. This is known as the Quantum Efficiency of the chip. The QE versus wavelength for various CCD sensors is shown above. The ATF sensor (a TC-215) is a front-side illuminated chip (anti-blooming normally turned off), while the IRO sensor (SITe 502) is a back-side illuminated chip with AR coating.

Blooming occurs when a CCD chip is overexposed. The overexposure causes so many free electrons to be produced that they overflow from the wells where they were trapped, and move into neighboring wells. The image at right is a picture of Saturn's which was intentionally overexposed to image the moons. This blooming can be irritating, if the target object lies above or below a particularly bright object.

There are two ways to avoid this problem. The first is to make a modification to the chip itself. This entails making ‘gutters’ between rows of readable pixels, so that the electrons can overflow into the gutter, and be carried off of the image. This method, however, causes a loss of 30% of the pixel area. This reduces both sensitivity and well depth, as well as the resolution! The quantum efficiency is also reduced, by nearly a factor of 2 in most cases. A second solution (the more common method for astronomical purposes) is to reduce the exposure time of your image, and take multiple exposures. These exposures can then be ‘stacked’, or added together with image processing software, to get an image with the required signal to noise ratio. Note that the signal to noise of multiple stacked images is the same as one image of the equivalent exposure time. Stacking images avoids the blooming problem, but can still overexpose the bright objects in the field. The main disadvantage of this method is the readout time of the chip. Taking many images is a much longer process than taking one long image (more about this later). However, many times this is not really an issue, especially for small private telescopes where the observing time is allotted at the discretion of the owner!

A CCD camera is a digital device, separated into pixels, each of which collects light, and liberates electrons. The number of electrons in each pixel is read off systematically by the computer, and later this number is converted into a grayscale (ADU, or Analog to Digital Unit) count, and displayed as part of an image. The read-off is accomplished in two steps. First, a row of pixels is shifted downward into a horizontal register. Then, this register is shifted sideways into an output amplifier. This process is depicted in the schematic at right.

To bin or not to bin is an issue you will have to decide for yourself. If you are in a location such as Iowa, where the atmospheric seeing is on average poorer than your pixel resolution, then binning is for you- no question about it. If, however, you are in a location with good atmospheric conditions, you will have to weigh the options. You may decide to bin for some projects, and not for others.

The number of electrons represented by each ADU count is called the system gain. A gain of 2.5 electrons/ADU indicates that each count or gray level represents 2.5 electrons. In general, a lower gain is better. However, this is only true as long as the total well depth (number of electrons that a pixel can hold) of the pixels can be represented. For example, suppose that each pixel in the chip can hold 85,000 electrons. A gain of 1.0 with this system would be low, but would also allow only 65,536/1.0 electrons to be counted. (2¹⁶=65,536) Some loss of well depth is not the disaster that it may seem, as cameras used in amateur astronomy are generally capable of only 13 bit performance due to the occupation of the lower bits by ‘noise’ (uncertainty associated with each conversion to ADU). High gains result in higher digitization noise. System gains are designed to be a compromise between the extremes of high digitization noise, and loss of well depth.

Correlated double sampling is a method used to ‘clear’ the readout pixel location before reading the next pixel value from it. The pixel is not actually cleared, but instead is flooded with electrons to a reference value. The pixel charge is then transferred in, and read out. The value assigned to this pixel is the difference between the reference charge and the readout charge. This method provides the best representation of the actual charge accumulated in the pixel.

There are two types of readout noise. The first type is due to the non-repeatability of the readout. The same charge in the same pixel will not always give exactly the same ADU count. This noise is intrinsic, and in most cases is very small. The second type of noise is the product of unwanted random signals from the sensor, the electronics, and the environment, which gets digitized along with the image pixel charge. Every analog to digital conversion circuit shows a distribution around an ideal conversion value. The sensor is the major contributor to noise.

All CCD cameras will liberate electrons over time. These electrons will collect in the pixels of the CCD camera. This process is extremely temperature dependent, and is the reason for cooling the CCD camera. The dark count is usually expressed as the number of electrons per unit time at a given temperature, and so is sometimes called the dark current. Corrections for the dark count can be made in the post-processing of the image, but the error in this method increases with increasing dark count. Thus the ideal method is to minimize the dark count present in the imaging system.

The dynamic range is the ratio of the maximum useable ADU count to the read noise. The ratio is usually represented using a decibel scale or as a power of 2 ('bits'). For example, a system with a well depth of 100,000 electrons and a readout noise of 12 electrons would have a dynamic range = 10 log 100,000/12, i.e. 39 dB or about 13 bits.

As the charge in each pixel is transferred through the system, some loss occurs. The charge transfer efficiency is the fraction of electrons successfully passed to the next position during the row and column readout.. The charge transfer efficiency is sensor dependent, and can be degraded by a poorly designed camera. The ideal efficiency is 1.0 (no electrons left behind). For example, the TC-215 sensor (used in the ATF's HPC-1 camera) has a CTE = 0.99990. Since there are 1024 shifts required to transfer the charge in a complete readout, the overall efficiency is 0.9999¹⁰²⁴ = 90%.

This test determines how the sensor responds to varying light levels over the well depth. An ideal CCD sensor should exhibit a linear response from the lowest detectable light level to the maximum well depth. For example, if a 1-second exposure produces 1000 electrons, a 5-second exposure should produce 5,000 electrons, and a 10-second exposure should produce 10,000 electrons. The response saturates when the well is full, as it simply can not hold any more electrons. At this point, the image has become overexposed, and blooming may occur.

The results of this test will be somewhat contaminated by the contribution of the dark current (recall that this grows with exposure time), but with an adequately cooled camera and relatively short (<5 seconds) exposure times, this should be a significant contribution.

If the CCD camera is already attached to the telescope, you will want to take flats of longer and longer exposure times. Flats are images of an out-of-focus, evenly illuminated source, such as a white piece of paper inside the dome.

If the camera is not attached to the telescope,

Dark count is a function of the CCD characteristics and the temperature of the CCD. The dark count will double with a rise of 5-6 degrees C.

The signal variance method of determining system gain in electrons per ADU is the most difficult of the tests discussed here, but can be repeated by anyone who follows the procedure outlined. This method is one where multiple exposures are taken with increasing light. Standard deviation and mean count data is collected for each image. The standard deviation numbers are each squared, then plotted with the net mean (mean - bias) numbers. The slope of the line represents the gain of the system. The test setup is very much like that discussed for the linearity test above.

If your camera is not attached to the telescope:

1. Set up the conditions as you did for the linearity test. The light will probably have to be brighter.
1. Stack several sheets (8-10) of plain white paper over the camera.
1. Take a series of pairs of exposures with a fixed short exposure time (e.g. 0.2 sec), but with successively smaller number of sheets of paper. The goal is to obtain pairs of images with ADU counts ranging from near the low sensitivity limit to the maximum ell capacity.
2. For each pair of images, use CCDsoft to subtract one image from the other after using the 'add constant' trick on the first image to avoid negative pixel values.
1. Use CCDsoft (or Camera) to record the mean and standard deviation of each differenced image. Be sure to subtract the constant used in the previous step before recording the mean ADU count.
2. Create a text file with two columns. In one column record the mean ADU counts; in the other record the variance (square of the standard deviation) for each differenced image.
3. Plot the variance versus mean ADU count on the X axis and the data on the X axis. Fit a straight line. The slope is the twice the gain in electrons/ADU. The intercept is (a poor) estimate of the read noise (after converting from ADU to electrons).

After determining the characteristics of a particular CCD camera, it is interesting to calculate the signal-to-noise ratio (SNR) expected using that CCD camera with a telescope of given aperture. The SNR is the ratio of the signal counts to the square root of the signal count plus all contributing noise effects. The fundamental equation is

where

1. N_e is the number of stellar photons per second at the CCD sensor:

and So is the number of photons per meter² incident on the telescope from a 0^th magnitude star (at 550nm) per unit bandwidth (nm), ignoring extinction:

3. N_sky is the number of electrons per pixel per second due to the background sky brightness. This can be calculated by knowing the sky brightness in magnitudes per arcsec² , adjusting for the pixels size in arcsec, and using the formula for N_e above.

4. D is the dark current in electrons per pixel per second, and R is the read noise (electrons). Note that the read noise [R] term is squared since the read noise is already

• ATF with the HPC-1 sensor (0.18m diameter refractor, HPC-1 has a QE of ~60%, sky brightness 16^th mag.) using a clear filter (filter width 500 nm).
• ATF, but with the Lynxx camera.
• The IRO using the SITe sensor (diameter 0.5m, R=10, D=0.1, QE=0.9, sky brightness 21^st magnitude).

2. Calculate and plot the SNR at the ATF (with HPC-1) for a V=18 star as a function of exposure time from 10 to 1000 seconds (use log-log axes). What is the limiting factor at short exposure times? Long exposure times?