Techniques of Observational Astronomy
AST3722C

CCD Observing

Full Well, Noise, ADUs, and Dynamic Range

Each pixel of charge (collection of electrons) is moved to a capacitor where it appears as a voltage. This voltage is read by an "Analog-to-Digital" (A/D) converter circuit which provides a numerical value to be transmitted to the CCD control and display software running in a computer. The numerical values are usually referred to as ADUs (analog digital units) and they usually are not simply equal to the number of electrons read out from the pixel. Rather, a "gain" factor is applied to that the largest number that can be produced by the A/D results from a pixel that has just reached its "full well" value. If the A/D is a 16-bit converter it can produce values between 0 and 2**16 (2 raised to the 16th power) - 1 or 65535. If the full well capacity of a CCD is about 40,000 then the gain would be set at about 1.6 ADU/electron.

Any process is subject to noise and the generation, collection, transfer, and A/D conversion of pixel charge is no exception.The "dynamic range" is related to signal-to-noise (S/n) ratio. If the total noise of the pixel charge signal is +/- 10 electrons rms (root mean square) and the full well capacity is 40,000 then the maximum S/N is 4000 and the "dynamic range" would be 4000 to 1. In this case a 12-bit A/D would suffice (2**12 = 4096) most modern CCD systems use 16-bit A/Ds anyway.

Bias and Dark Frames

• A CCD image will be built up from three signal sources
  • object: photons imaged onto each pixel of the CCD
  • dark current: thermal electrons collected in each pixel during the exposure
  • bias: a low level electrical signal added to each pixel during image readout

Darks

In order to remove the accumulated background due to thermal dark current, it is usual to take one or more "darks" which are images taken with the CCD camera shutter closed. These darks should be of the same exposure time and camera temperature as the object exposure to be dark subtracted. Since the accumulation of dark current is a mostly random process, it is best to take a set of dark images and then to combine them to get a "master" dark based on the average of the dark set. [Note: it is usual to "median combine" as will be discussed when we cover statistical methods.]

Bias

In addition to thermal noise, each pixel charge will carry with it a fixed offset voltage value called the bias. Thus even if the output coming from the CCD were exactly zero electrons for every pixel, there would still be a signal that would vary from pixel to pixel in a repeatable fashion. An bias frame is one taken to determine this bias pattern. In principle a bias frame is simply a zerosecond dark exposure. In the case of the ST-8E CCD used at the RHO 18 inch telescope we can not take a zero second exposure (the shortest possible exposure is 0.1 seconds). If we want a bias frame (but see later ... we probably do not need one) we can get a reasonable approximation by taking a 1 second dark exposure and a 2 second dark exposure. Since the bias pattern will not change with exposure time, we can multiply every pixel value of the 1 second exposure by 2 and then subtract the 2 second exposure, pixel by pixel. That is 2*(1_ second_dark+bias) - 2_second_dark+bias = bias.

Because noise is a statistical process sometimes an added fixed value "bias" is added to make certain that the voltage presented to the A/D convertor is never negative. The ST-8E CCD used at the RHO 18 inch telescope has 100 ADU added to every output number for this reason.

Flat Fielding

Each pixel on the CCD may have a different sensitivity to incoming photons due to small variations in individual pixel dimensions and quantum efficiency. For precision photometry it is necessary to calibrate such pixel-to-pixel variations and this is the function of "flat fielding". There are several different approaches but the two that are applicable to most observatories are

• Dome Flats: A uniformly illuminated target is installed in the dome or attached to the front of the telescope

• Sky Flats: Images are taken of the sky which is assumed to be uniform in brightness over the (usually small) field of view of the CCD

Dome Flats

To understand the procedure for flat fielding, one must recall that all incoming light rays that are parallel to the optical axis are imaged by the telescope optics at the center of the image (assuming everything is properly aligned). Ray that strike other parts of the image do so because they are entering the telescope at some angle to the optical axis. Since the field of view of the typical CCD is measured in minutes of arc, only rays whose angle to the OA is some small number of minutes of arc hit the CCD. Thus (to a first order)it is the uniformity in intensity of the rays from the flat field target as a function of angle that must be (nearly) constant, not the variation in intensity from point to point on the target. A typical illuminated target will be a Lambert's Law surface (I varying as cosine theta) so over a range of 15 arc minutes the variation will be less than 0.5%.

Notes based on an essay by Michael Newberry, Axiom Research, Inc.

• The Problem
  • Dealing with response variations from pixel to pixel in CCD images due to
  • Optical vignetting (typically symmetrical with optical axis)
  • Penumbral shadows of dust specks and optical flaws
  • Pixel to pixel sensitivity variations
  • Shutter travel time shading
• Solution
  • Take an exposure of a source which will uniformly illuminate each pixel of the CCD
  • Pixel sensitivity (and perhaps other effects) will be a function of wavelength so separate flat fields are needed for each filter
  • Use a long enough exposure time to fill pixels to more than 50% of their full well capacity (Pixel sensitivity should not be a function of exposure time while in the linear region of CCD response)
• “Flat Field” types
  • Twilight Flat: Exposures of the twilight sky (effectively a uniform source over the small area of the CCD chip if imaged well away from horizon). Can correct for all of the types of sensitivity variations but the twilight sky is typically much bluer than the typical program object. Does well to correct vignetting and penumbral shadows if gradient with time is controlled (difficult to do … sky changes very rapidly)
  • Dome flat: Exposure of a special target, usually mounted on the dome (such a target is completely out of focus and thus effectively uniform) Does well on Pixel to Pixel variations, poorly on vignetting and penumbral shadowing. Some care must be taken to get long enough exposures and correct spectral range (need a high color temperature light source such as a Halogen lamp)
  • Sky Flat: Median combination (to remove stars) of many exposures of the night skyGood correction of vignetting and penumbral shadowing, poor correction of Pixel to Pixel variation. Hard to get enough photons on CCD … exposures may be very long.
  • “Dithered Flat”: Many (8-15) images of a field, displaced 10 - 20 pixels randomlyRegister the images in software. Each portion of the image is exposed on many different sets of pixels. Vignetting and Penumbral Shadows must be removed before combing images. This method deals with Pixel to Pixel variations very well.
• A Systematic Approach
  • Do Dark and Bias corrections for each image
  • Take a number of long exposure (>= 5 to 10 seconds) twilight flats.
  • Average or median combine the twilight flats in software
  • Smooth with a large area filter (say 25 x 25 pixels) to remove pixel to pixel variations
  • Normalize to 1.00 at the center
  • Save as a 32- bit real image
  • This is your “illumination flat”
  • Make a number of dome flats through each filter.
  • Average or median combine to get high S/N image
  • Make a copy and smooth with a large area filter (say 25 x 25 pixels) to remove pixel to pixel variations
  • Divide high S/N image by smoothed image
  • Normalize to 1.00 at the center
  • Save as a 32- bit real image
  • The result is your “pixel flat”

Examples of Flats

An animation of a sequence of "Mystery" Flats

Summary

• Start with raw image
• Subtract dark and bias images (but see note on bias later)
  • use high s/n “master” bias and “master dark” frames for best results
  • master "dark" may actually be "dark plus bias"
• Divide by flat field
  • use high s/n “master flats” for best results
  • flats must have dark and bias removed

Different Considerations between "big" observatories and "small" observatories

Although the basic principles are the same, observers at "small" observatories such as our Rosemary Hill Observatory have somewhat different concerns from those important at "big" observatories.

Major differences:

• "big" observatories are usually on mountain tops in very dark sky locations
• "big" observatories usually cool their detectors with liquid nitrogen similar cryogen

The result is that at an observatory such as Kitt Peak or Cerro Tololo dark current and sky background become much less, and bias becomes an important source of background and noise in images. At an observatory such as RHO dark current and sky will be the dominating background and noise sources and bias can be effectively ignored except under very special circumstances.

Useful Links

Problem CCD Images

This page was last edited October 19, 2004 1:16 PM