Sub-Exposure Calculator
John Smith
November 12, 2004

Introduction
The accompanying calculator gives an analytical approach to determining the minimum exposure time for image acquisition. This calculator is conservative in that it uses the Kodak-specified values for mean dark signal. That dark signal is skewed a bit due to the small population of hot pixels.

In order to effectively use the calculator, you will need some data.

I. Gain (g): For SBIG cameras, this is measured at the time of camera manufacture and entered in the camera’s firmware. It is reported in the FITS header as the value of the keyword EGAIN. Consult your camera control program’s documentation for instructions on how to access the FITS header information. For other cameras or to verify the value, this value can be calculated by four frames. You will need to perform measurements in your camera control program to make this measurement. Here are the steps to measure the gain for your camera:

  1. Take two flat frames and two bias frames with 1x1 binning.
  2. Crop all four frames the same so that you have the same central approximately 25% of the frame. Make sure you do not include any cosmic rays or other artifacts in the cropped area. You want use as smooth an area as possible to prevent skewing the statistics.
  3. Measure the mean value of all four frames. Call these values F1 and F2 for the flat frames and B1 and B2 for the bias frames. Record these values.
  4. Using pixel math or image math as appropriate for your software, subtract one flat frame from another. Measure the standard deviation of the difference. See Note below. Call this value SDF.
  5. Using pixel math or image math as appropriate for your software, subtract one bias frame from another. Measure the standard deviation of the difference. See Note below. Call this Value SDB.
  6. Calculate the gain by using the following equation:
     


    Note:     Many programs do not handle the negative numbers that result from subtracting two similar images. In order to get the standard deviation of the difference accurately, proceed as follows:
    a. Add 2000 counts to the first image
    b. Add 1000 counts to the second image
    c. Subtract the first image from the second image. The standard deviation ignores the added values and gives an accurate value for the standard deviation.

II. Readout Noise (Ron): You can either use the default value of the calculator or measure your own camera using the following steps:

  1. Use the SDB value from the gain measurement, above.
  2. Calculate Readout noise by using the following equation:



III. Sky Flux (Esky): Take a 3-minute test exposure of a star poor area of the sky. Don’t worry about guiding, star trailing, etc. It is best to take this image near the zenith to minimize the impact of any light pollution gradients. Of course, the moon should not be in the sky. Once the image is obtained, perform the following steps:

  1. 1. Dark subtract the image using either the autodark function of subtract a master dark.
  2. Measure the ADU of the sky, between the stars. You can use either an aperture tool or the cursor, depending on your software application.
  3. If you are using a program that adds a 100 ADU count to avoid negative values, Maxim and CCDSoft are of this kind, you should subtract 100 from the value you obtained in step two. If your program can handle negative values, it most likely will not add the 100 count value. Mira is an example of this kind. This is the Test Exposure Average Background (ADU).

IV. Analysis: With the above data, proceed with the following steps:

  1. Select your camera from the pulldown. If your camera is not represented, you will need to get information for you specific chip from the manufacturer.
  2. Enter the values obtained above for readout noise and gain.
  3. Enter your desired camera operating temperatures. It is instructive to select some different operating temperatures to see the effect on the number of dark sub-exposures you will need.
  4. Enter your Test Exposure Average Background from III, above.
  5. Decide how much you will allow readout noise to contribute to your total noise. Acceptable values are 5-10%, depending on the number of sub-exposures you want to take.
  6. Decide how much you will allow noise from your dark frames to contribute to your total noise. Since darks are cloudy night activities, don’t limit yourself to a few darks. This is an easy way to reduce darks. Start with 0.5%.
  7. When the data is entered, hit the update button.
  8. You will see displayed the recommended sub-exposures, based on the above data. Additionally, you will see a recommended number of dark frames, depending on how you combine your darks.

V. Discussion:

Try different values of Allowable noise contribution from readout noise and dark current noise. Note how temperature tends to reach diminishing returns as your camera gets down to -20°C to -25°C. Note how the method of combining impacts the number of darks required. Min Max Clip is a combining method used in Mira. Similar results can be achieved by using Ray Gralak’s Sigma program (www.gralak.com/Sigma)

You should repeat the calculation for each filter you use and each binning you use.

Note that narrow band imaging hardly ever gets to a sky noise limited condition without very long exposures. Here, 10-20 minute exposures at 1x1 binning are generally the norm. However, if you are interested in broad area narrow band information such as clouds of nebulosity, then 2x2 binning can help significantly in getting to a good SNR.

Lastly, dithering is an excellent tool to significantly improve your overall SNR.

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