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In the Basics of CCD Imaging section, a simple dark frame was used to calibrate the images.  Subtracting dark frames is the most important calibration process, but flat fields can also be critical.  Bias frames are only used in certain situations, but they are discussed below.  And there are ways to improve upon the basic dark frames.

Dark Frames

The noise in a CCD image is dependent primarily on the temperature of the camera.  A dark frame taken at the same temperature as an image, therefore, will have approximately the same noise, making it possible to subtract this noise from the image.  However, there are still slight variations in the amount of noise from dark frame to dark frame.

A common technique is to take multiple dark frames at the same temperature and then combine these to get a better model for the noise in an image.  This will also tend to cancel out any slight variations in temperature between the images.  Using a median combine method (or similar) also allows noise sources such as hot pixels from cosmic rays to be removed, further improving the noise reduction vs. a single dark frame.

There are a couple methods for the use of multiple dark frames.  One is to simply take a set of images, save them individually, and then combine them later as you would individual light images.  Some software packages allow you to select multiple files for dark calibration and the combining is done automatically.

Remember, dark frames must be equivalent to the regular light frames in every respect.  The exposure length, temperature, and binning must all be equal.  The noise characteristics of a camera are dependent on exposure length, temperature (colder = less noise), and pixel binning.  Changing these parameters between lights and darks will cause a mismatch between images and the noise removal will not be ideal.

 

How Many Dark Frames?

How many darks you take depends on how little you want the noise contribution from dark current to be.  Even just taking 3 darks can lead to a noticeable improvement over a single dark frame.  The noise contribution is a function of the exposure time, camera characteristics, and operating temperature, as well as the combining method used, but there are some general guidelines.  Based on calculations by John Smith on his website (an excellent resource for CCD imagers), for a typical camera/exposure combination, 3-4 darks gives approximately a 10% contribution from dark noise.  6-8 darks reduces this amount to 5%, and to obtain a 1% contribution, 20-30 darks must be used.  Most of the images used in the Guide to CCD Imaging website examples were dark subtracted with a single dark frame, or a combination of 3 darks.  For more critical applications, 10 or more darks are recommended.

Tip:  Dark frames can be taken after the light images.  In fact, they can be done while you start packing up other equipment, or when clouds roll in, etc.  This way you don't waste precious imaging time taking calibration images.

 

Flat Fields

Flats are used to remove image artifacts due to the optical system.  Vignetting and shadows from out-of-focus dust specks are the most common aberrations which flats eliminate.  A flat is simply a blank, evenly illuminated image which will show the variations in brightness due to the optical system.  By subtracting this image from the uncalibrated celestial image, these aberration are removed.

There are a number of ways to take flat frames.  Sky flats are taken by aiming the telescope at the post-sunset or pre-sunrise sky.  The twilight sky provides a blank, evenly lit source for flat fields.  However, stars appear in the image well before you can see them visually, so there is a narrow time frame available for capturing the images.  Also, you must either be set up to image before dark, or stay up until just before sunrise.  Another method involves shooting an image of an evenly illuminated surface set up near the telescope (or in your observatory).  The image is ideally unfocused, so something 5 or 10 feet away is fine.  Some imagers even construct light boxes which mount over the front of a telescope and have a built-in light source.  This works fine but is probably more precision than is necessary for most imaging.

A flat field is taken with the camera in the same position it will be in for imaging.  Any rotation of the camera or auxiliary optics (such as a focal reducer) added or removed between flats and light images will affect the usefulness of the flats.  The brightness of a flat should be within an ideal range.  The usual recommendation is to end up with average pixel values in the image of about 1/3 to 1/2 of the saturation value of your CCD.

The saturation value of a CCD camera is a function of the full-well capacity and the gain.  It is therefore not necessarily the same as the maximum pixel value.  For example, an ST-237A has a max pixel value of around 65,000 e-.  However, the saturation level is only 9,000 e-, or a pixel value of about 3800 ADU.  The recommended flat value would be between 1250 and 1900.  Note that for some cameras, the calculated saturation value is greater than the maximum pixel value (65,535 for a 16-bit camera).  For such a camera the recommended flat field value would be 1/3 to 1/2 the max pixel value, or 21,845 to 32,767.  Use the chart below for some common cameras, or visit the CCD Calculators Page to determine the recommended flat value for your CCD camera.

CCD Camera

Saturation Level (e-)

Recommended Flat Value (ADU)

ST-402ME

43,500

7,400

ST-7/8 ABG

21,700

3,300

ST-7/8 NABG

27,800

4,300

ST-10ME

59,000

18,000

ST-2000XM

65,500

26,200

SXV-H9/H9C

60,000

26,200

 

Measuring ADU Values

Measuring the background ADU values for a flat field is easy.  Take a test flat image at a known exposure length, say 1 second.  Software packages will allow you to measure the background value.  MaxIm DL, for example, will tell the pixel value (in ADUs) by simply moving the cursor over the image.  Data is displayed in the lower right-hand corner of the screen, and the value "i" indicates ADU count.

Above:  Pixel data in MaxIm DL.  The background pixel value is 12,319.

Suppose your camera requires a flat field value of 18,000, and a 1 second exposure yields a value of 12,000.  You need to increase the exposure by 50% to 1.5 seconds to get a value of 18,000.

Above:  A typical flat field image showing slight vignetting as well as dark halos from dust specks in the optical path.  This image is a sky flat, taken just after sunset.

 

Taking Sky Flats

For wide field imaging, it is critical to shoot flat fields using an evenly illuminated section of the twilight sky.  The sky brightness displays a gradient toward and away from the position of the sun.  The best location in the sky for taking flats is an area just east of the zenith.  This null area of the sky exhibits the least brightness gradient (Chromey and Hasselbacher, 1996).  Away from this point the gradient can be 5% per degree or more.  For critical applications where ideal flats are necessary (such as photometry), this can be problematic as variations in the background ADU count can vary by several thousand.  For pretty pictures, this is less critical, but pointing to the zenith or slightly east will result in sufficient quality flats.

Tip:  When taking twilight flat field images with a digital SLR, allow the camera to automatically meter the proper sky exposure and you will achieve a good result.

 

Bias Frame

Bias is the term used to describe a CCD camera's pixel-to-pixel variation in zero-point.  Each pixel has a slightly different base value, and this bias is removed using a bias frame.  Since dark frames contain the same bias as a light frame, dark-subtracted images are already bias-subtracted.  But some new cameras do not require dark frames, as they have very low dark current, so a bias frame could be used for images taken with such a camera.  Also, a bias frame can be used to scale a dark frame in the event that a dark frame is not equal in exposure time to the light frame from which it will be subtracted.

A bias frame is, ideally, an exposure of zero length.  Since a zero-length exposure is not allowed by imaging software, simply use the shortest possible exposure time.  This is usually 0.01-0.1 second.  Be sure the camera is at the same temperature as the dark frames which will be scaled with the bias frame (which should, in turn be equal to the temperature at which the light images were taken).

Usually, three or more bias frames are used to reduce noise in the same way multiple darks are combined.  These are later median combined either before being used to calibrate the image, or automatically during the calibration if your software allows.

Above:  A typical bias frame.

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