Pushing the Envelope ... CCD Flat Fielding

HET609 2003

Jose Ribeiro

Introduction

Since 1975 astronomers have been using CCDs to obtain scientific images. These sensors allow images of lower noise, comparatively to other sensors, a band-pass of 300 to 1050 nm and an efficiency superior to other image sensors (photographic emulsions, image intensifiers, etc.).

In order to obtain images of scientific interest, these should be normalised. This means that images of the same object obtained by different equipment and persons should contain the same information. Therefore, a set of procedures, known as image reduction, should be followed:

- Acquisition of bias or dark image

- Acquisition of the flat fields

- Aquisition of the images of the object of interest

The bias image is obtained by reading the CCD not exposed to light, with a null time of exposure. This image represents the noise caused by the amplifiers of the CCD and is constant in time. An average of ten or more single bias frames must be done.

In case the CCD camera is not properly cooled, the dark frame should be used instead of the bias frame, because the thermal noise (dark current) is relevant. According to Howell, “at room temperature the dark current of a typical CCD is near 2.5x10⁴ electrons/pixel/second”. With cooling by liquid nitrogen these values decrease to 2 to 0.04 electrons/pixel/second. The dark frame is obtained by exposing with the shutter closed, with a duration equal to the one of the image of the object of interest. The dark frame already contains the bias data.

The flat field images, the subject of this essay to be developed hereafter, are used to normalise the capacity of photon capture of each pixel of the CCD array. In fact, the pixels of the CCD sensor have quantum efficiencies (capacity to transform photons into electrons), different from pixel to pixel. Basically, the image acquisition of the flat field consists in illuminating the CCD in an homogeneous way and to make an exposure with a duration as high as possible without the pixel response becoming non-linear. Several images must be taken and averaged.

The image reduction consists in subtracting the bias or dark frame to the raw image frame of the object of interest and divide it by the flat field image previously subtracted by the bias or dark frame image:

I_Reduced = ( I_Raw– I_Bias) x M / (I_Flat- I_bias )

Where I_BiasMay be the bias image or the dark image and M is the average pixel value of (I_Flat- I_bias ) [5].

From all these calibration procedures, the most delicate one is unquestionably the acquisition of the flat field image.

Flat Fielding

As mentioned above, flat fielding is used to correct the non-uniformities in quantum efficiency between the pixels of a CCD. Yet, other corrections are included in a flat field frame [1]:

- Dust particles on CCD, seem in the flat field as small sharp dark figures

- Dust on the optics and filters seem in the flat field as torus shaped features

- Vignetting, seem as darkening towards the edge of the telescope field of view (see image)

One must point out that the efficiency of the correction of these defects implies that the set-up must be unchanged from the acquisition of the flat field to the acquisition of the images of interest. As these three situations are bound to change during the observation time, namely more dust, fingerprints in the optics, bat droppings, etc.), flat fields should be done before and after the night observation.

When determining the flat field corrections, one should take into account two major premises:

- Illumination should be homogeneous in all points of the detector, and should be brighter than any image to be observed.

- As CCDs have different sensitivities in function of colour, the colour of the light falling at the detector must be the same as that in the observation. One flat image must be done for each filter used.

To follow these premises is not an easy task. To obtain an homogeneous illumination is practically impossible, becoming more difficult as the field of view enlarges due to the effects of scattered light [6]. On the other hand, the illumination used to obtain the flat field is different from the night sky; so, the colour correction is far from being perfect. In infrared observation, one can use the night sky (bright at infrared wavelengths) to establish the flat field, under the disadvantage of loosing precious observation time.

Several types of flat field methods are usually used, being the more common ones the dome flats, the sky flats, and the projection flats, being the latter used in slit spectrometry.

Dome flats

Dome flats are acquired by aiming the telescope to an illuminated zone in the dome or to a screen placed inside the dome. The method procedure is as follows:

- Some frames are done to the homogeneously illuminated zone of the dome of the screen with an exposure time adequate in a way that the pixels will remain in the non saturated zone but with a good sound to noise ratio. Here, some authors defend “at least 25% full scale” [5], whereas others defend that “the number of counts should not exceed 80% of the saturation level” [9].

- Bias or dark frame are subtracted to each dark frame.

- As the dome is not impermeable to the cosmic rays, these should be removed from the flat frame. For that, the several flat frames should be combined by taking the median level at each pixel.

- Normalise to unity at the normalisation point. The normalisation point may be a “cosmetically cleaned region on the fiducial CCD” [8].

The main advantage is the fact that the flat fields can be acquired during day time, leaving night time exclusively for observation. Another advantage is the fact that with this method greater sound to noise ratios are obtained [7].

The main disadvantages of this method are:

- The spectral distribution of the lamps used in the illumination is different from the spectral distribution of the sky. This fact is more relevant for observations done with broadband filters than with narrow band filters, and may cause fringing. The fringing is an interference pattern resulting from reflections of the incident light inside the CCD substract. [1][10].

- The reflected light from the dome or from the screen reaches the telescope in a different angle than the incoming light from the sky. This may move the position and change the shape of the dust features and of the vignetting in the flat frame.

- An uniform illumination of a dome screen is difficult to obtain [7].

- “The use of dome flats alone will leave a low frequency non-flat scaling in the images” [4].

Usually, dome flats may be combined with sky flats.

Sky flats

Sky flats are obtained by aiming the telescope to the sky. The suitable time will be a twilight sky at dusk or dawn, but they may also be obtained during night sky for infrared observation, as in infrared the night sky is bright enough to guarantee a good signal to noise ratio [1].

Exposure times, as for the other methods, should allow a good signal to noise ratio and not reach the point of non-linearity of the CCD pixels.

The way of image capture varies from observatory to observatory. Some defend that the telescope must be tracking during the frame acquisition, but must be offset between exposures [8]; others defend that the telescope should not be tracking (Swinburne).

Hence, the treatment procedure should be carried on in the same way as described above for the dome flat.

This method has the advantage of having an illumination with an angle equal to the one of the observation; so, the problems occurred in the dome flats regarding dust and vignetting do not exist. On the other hand, the illumination by sky has a better colour balance than the illumination by artificial light. “The best calibration observation is of a blank sky” [3].

Some issues exist in this technique. The more important is due to the fact that at twilight the sky brightness is not uniform and changes quickly. This causes the problem of the non uniformity of brightness in each frame, which will increase with the field of view. For the same reason, there will not be two similar frames, because during the time of reading of the CCD, the sky brightness has changed in the meantime, and this will be a more serious problem when the reading of the CCD is slower.

Stars can also interfere in the quality of the flat frame. Yet, in the posterior treatment the combination of frames by taking the median level at each pixel will free the data from stars and cosmic rays. Defocusing the telescope to smooth the effect of the stars is not advised, because a change in the focus may induce a change in the vignetting [1].

And the last, but not the least, the purpose of profiting the usually short and rare time of telescope should be to observe the object of study, and so the acquisition of the sky flat correction should be extended into the observing time. Therefore, the available time for the acquisition of the twilight flats is indeed a short one.

Flats for spectroscopic work

For spectroscopic work, flats must be taken by direct projection of the light into the spectrometer’s slit. The reason for this is that normal sky light or even reflected light from a dome or screen, would be dispersed in the spectrometer and the low signal would not be enough for a good signal to noise ratio. The major problem in flat acquisition for spectroscopy is the fact that the spectrum of the lamp may coincide with the spectrum of the observation. Dividing the science frame by the flat will introduce the inverse of the spectrum and transmission in that frame [3].

Flats in space work

In the space there are very few possibilities of making flat fields. In this case, the usual solutions are the creation of high sound to noise ratio flats in laboratory (Howell). In the case of GAIA mission it is said that the images of the same object will be taken at different positions and position angles. In this case, the image averaging will attenuate any inter-pixel non-uniformity, “reducing flat fielding errors to negligible errors” [2].

Electro-optical tracking methods

When the telescope has not the tracking capability, as in liquid mirrors, two methods exist to allow some sky follow-up: drift scanning and time-delay integration (TDI). In both methods, the CCD is continuously read at a slow rate, in a way that each point of the sky will be sampled for an equal time by every pixel in a column of the CCD [12]. This means that each pixel of the final image is the result of the mean efficiency of all the pixels in the column. Therefore, the pixel non-uniformities and hence the flat fielding errors along the column will be negligible. A correction must be done for the non-uniformities between columns but, according Gibson and Howell, a one-dimensional calibration image will do the job more easily and accurately.

In the drift scanning method, the CCD is mechanically moved to avoid image smear.

In the case of TDI, the detector is fixed and is read at sidereal rate. The detector must be oriented so that the array is properly aligned with the motion of the sky.

Both methods have limited integration time, which depends on the size of the CCD. For the same sensor, TDI integration time will be shorter because the CCD is fixed; in drift scanning, the sensor can be moved and track the sky.

In both methods, the resulting images will show an elongation oriented East-West, due to the fact that the shift in the CCD is discrete whereas the image moves continuously across the array [12]. TDI method will be additionally a distortion (asymmetric North-South elongation), due to the fact that only at the celestial equator the sky paths are rectilinear, increasing the curvature with declination. In the case of the drift scanning, the mechanical movement of the sensor may compensate for this error.

While with a good conventional flat field correction one can obtain an accuracy slightly lower than 1%, in the case of the drift scanning or TDI one can obtain correction with an accuracy £ 0.1%.

Conclusion

From all the steps towards a good normalisation of data acquired through CCD sensors, the most complex and controversial one is the flat fielding correction. There is not an optimal method. Each observatory has its own procedure for the flat field acquisition.

For direct observations, sky exposures provide a better spectral correction despite of the limitation in the field of view; also, dome flats are used basically for back-up of sky flats [4].

Regarding spectroscopic work, the preference goes to the projection flats.

The methods of drift scanning and TDI, although of limited utilisation, produce the best results. New algorithms and techniques must be developed in order to correct the drawbacks found on these methods.