Flat-Field Frame Calibration

Each pixel in the camera has a slightly different sensitivity to light. These sensitivity differences add another noise component to the image (known as flat-fielding error) unless steps are taken to compensate. While flat-fielding correction is important for achieving good quality images, it is absolutely essential for accurate photometric measurements.

With a bright sky background, any pixel-to-pixel variations in sensitivity are imprinted into the image; the more sensitive pixels show up as brighter dots. Unless you have a space telescope you will always have sky glow; natural atmospheric emissions ensure some sky glow even at prime observing sites. When long exposures are used to detect extremely faint objects, much fainter than the sky glow, the ultimate sensitivity limit is determined by how precisely the flat-fielding error can be removed.

There are several common sources of flat-fielding variations. Typical sensors have pixel-to-pixel variations on the order of 1%. Vignetting in the optical system can reduce the light flux at the corners of the sensor. Dust on optical surfaces near the sensor can cast shadows (often called ”dust donuts” due to their appearance in centrally-obstructed optical systems). While compressed air can help reduce dust donuts, it is often difficult to completely eliminate them.

To create a flat-field frame, the optical system is illuminated by a uniform light source and an exposure is taken. To avoid non-linearity at the top and noise at the bottom of the camera's range, the exposure is usually chosen to get an average value of 30% to 50% of the saturation level. The flat-field is then renormalized by dividing each pixel into the average value in the array. Any pixel that is more sensitive will be assigned a number slightly below 1; any pixel that is less sensitive will be assigned a number slightly above 1. When this frame is multiplied by a raw image, it removes the sensitivity variations.

Acquiring Flat-Fields

Flat-fielding is by far the most troublesome calibration method. The entire aperture of the optical system must be evenly illuminated with light – if this is not done very carefully, then the flat-field will be wrong. Light leaks will ruin the calibration by adding unfocussed light that did not pass through the optical system. Once calibrated, the camera cannot be moved or even refocused. Some sensors have significant flat-field variation as a function of wavelength (color), and it can be difficult to create a reasonable facsimile of the normal illumination spectrum. Given all these problems, a good flat-field can be very difficult to achieve in the field, and so this calibration step is sometimes skipped.

If there is no vignetting and dust donuts are not an issue, calibrating the camera alone may be sufficient. Cover the end of a roughly six-inch long opaque tube with a translucent material (a few layers of white photocopy paper will do in a pinch). Place this over the front of the camera, gently illuminate the assembly with white light (natural or incandescent, not fluorescent or LED), and take an exposure which produces a brightness level of roughly 30% of full scale. The resulting images can be used to flat-field the camera, regardless of the optics used. Note that the window must be very clean (no dust spots) for this to work properly.

A common technique for astronomical applications is to use ”twilight flats,” where the twilight sky is used as a diffuse light source. Rapidly changing light levels can be troublesome, but the illumination can be very uniform if care is taken to avoid recording stars (or to remove them by shifting the telescope between exposures and using sigma clip with renormalization, which MaxIm DL's calibration tools can do automatically). A more advanced technique is to use ”sky flats.” This is described in more detail below.

The flat-field frames themselves must be calibrated to remove bias, and for longer exposures dark correction must also be performed. It is essential that both the flat-field frames and light frames are properly bias corrected; otherwise the flat-field operation will not work correctly (mathematically, subtraction and division are not commutative).

You do not need to worry about the mechanics of bias correction and renormalization when using MaxIm DL. The calibration tools know how to handle this automatically.