Flat Field for Film Images - A Cheating Method

Film flat fielding is extemely difficult. Because of the nonlinearity of film, standard CCD flat field method just doesn't work. In most of current methods for film flat fielding, a model for flat field has to be generated from the astronomical image itself. This model is then applied (subtract or divide) to the image to correct for the effect of vignetting. Generating such a model needs "background" regions in the image where there are no stars and nebulas. In many deep images, however, there are almost no background regions and the flat field models are not perfectly reliable.

Here I introduce a new flat field method. In this method, no background regions are required and therefore it is especially suitable for crowded, deep images. I should point out that I never said this method is reliable. It doesn't have the problems caused by the lack of background regions but it may have its own limits.

This method is called cheating method by me. Suppose we have an image taken by a telephoto lens and it suffers from vignetting. We can use another image taken by a much wider lens as a reference to remove the vignetting in the telephoto image. The reason why this works is that illumination in a small area of the wide-field image is usually quite uniform. Below I will use an example to illustrate this technique. This is a very quick and dirty example. Once you understand the basic idea, you should be able develop a much more sophisticated work flow be yourself. In other words, don't view below as a step by step guide. It's just to show you the idea.

The image to be flatten is taken and provided by Mr. Thomas W. Earle.

A = original image	B = reference image

Above shows the original image taken with a 300mm 67 lens by MR. Earle. The reference image was taken by me, using a 80mm 645 standard lens. The standard lens image was registered and calibrated to the 300mm image in Registar. Before the calibration, a minimum filter was applied to the reference image to reduce star sizes. This helps Registar to obtain better calibration. In addition, the reference is only calibrated to the central protion of the original image. You can move the mouse over the reference image to compare it with the original.

After the reference image was registered and calibrated, both the original image and the reference image were heavily minimum and median filtered to remove most of the stars. Then the two filtered iamges were subtracted (orignal-reference). Below shows the result of the subtraction (C).

C = (filtered A) - (filtered B)	D = max(C)

Image C is the subtracted image, with a strong gamma stretch to show the faint light better on the webpage. As shown in the image, there are lots of dark spots. I believe this is because the stars in images A and B have difference sizes and they don't cancel each other perfectly. To fill in the dark holes, I used a large radius maximum filter. The result is C. This is the flat field model, a very ugly one. To make it better, I manually remove the remanent features from bright stars (Deneb) and red nebulas. Then I blurred the model with a large radius Gaussian. I also assume the illumination pattern to be corrected is symmetric about the image center. (Apparently it is not, but....) By assuming so, I can average the image with its mirror and then with its 180 degree rotation. The final model is shown below.

F = final flat field model

Since F was made from A - B and B is supposed to be vignetting free, the vignetting corrected image should be A-F. This is shown below. You can move the mouse over the image to see the difference between the corrected image and the original.

G = A - F

There are a few things to note.

1. The artifacts in image C is caused by the different star sizes in the two images (original and reference). Apparently, the resolution of the reference image needs to be as similar as possible to the original image. In other words, the focal lengths of the lenses that take the two images should not be very different. I suggest the difference between focal lengths should be within factor of 5.

2. In addition to focal length, the reference image should also be taken with identical film and with identical processing, in principle. In this example, the 300mm image was taken with E200 and the wide-field image was taken with E100S. This difference is partially why the nebulas in the two images don't cancel each other perfectly, even after a calibration in Registar.

3. Here I used the subtraction based flat field method. The only reason of doing so is that it's easier for Photoshop and I wanted to do it quickly. With a software that can do division (such as PixInsight LE), it is possible to develop a division based method.