172
12 High-Precision Differential Photometry
is a good project as an introduction to astronomical programming and FITS manipulation.
The combined contribution from dark and bias noise is likely to be insignificant,
and one would expect it to be significantly outweighed by noise from the flat-field
frames and the sky. If, however, you do have a high-level noise in the dark and biases,
there are several things that can be done to address them.
Firstly, check that your analysis of the errors is correct, for example by performing the same operation on files from a good instrument. For example, data can be
downloaded from the ESO website. If the uncertainty is real, then it is best to dismount the instrument from the camera and test it in a lab, away from any electrical
noise source. If possible, try replacing the camera power supply and data cable with
a known low-noise version. If in this setup the noise becomes low, it is most likely a
faulty power supply or cable. If the noise persists, then it is likely an inherent fault
with the camera, which might not be easy to resolve.
12.3.1 Flat-Field Noise
Flat-field noise cannot be directly measured, as the noise is the variation in the flatness
of the image frame after the application of the flat field.
The noise in a calibrated frame is given by
σ cal =
σ
2
Bias + σ
2
Dark σ
2
Flat ,
(12.1)
which we can rearrange as
σ Flat =
σ
2
cal − σ
2
Dark − σ
2
Bias .
(12.2)
Hence, we can get to the flat-field noise by measuring the noise in a calibrated
frame. Ideally, you need a calibrated frame that has few stars in the image. The noise
within the frame will have to be measured away from any star or other astronomical
objects in the field, although this is not a problem for dome flats. Again, this may be
achieved by sigma clipping the calibrated frame, or the region function of SAO DS9
can be used to select and analyse a region of the calibrated frame free from stars.
By applying (12.2), we obtain the flat field noise σ Flat . You may wish to use multiple
images and multiple flat-field frames to obtain a more accurate uncertainty reading.
Poorly implemented flats-field frames can be a significant noise contributor. Good
flats take a considerable time to undertake, and if twilight flats are being used, the
area of the sky selected is often suboptimal and may vary in brightness. Although
sky flats are normally considered the best method to obtain flats, improvements in
flat-field lighting sources have closed the gap between sky flats and dome flats.
A typical dome flat is taken using the inside of the dome. This is unlikely to be a
uniformly reflective surface, and the dome lights are unlikely to have a flat spectrum.
12 High-Precision Differential Photometry
is a good project as an introduction to astronomical programming and FITS manipulation.
The combined contribution from dark and bias noise is likely to be insignificant,
and one would expect it to be significantly outweighed by noise from the flat-field
frames and the sky. If, however, you do have a high-level noise in the dark and biases,
there are several things that can be done to address them.
Firstly, check that your analysis of the errors is correct, for example by performing the same operation on files from a good instrument. For example, data can be
downloaded from the ESO website. If the uncertainty is real, then it is best to dismount the instrument from the camera and test it in a lab, away from any electrical
noise source. If possible, try replacing the camera power supply and data cable with
a known low-noise version. If in this setup the noise becomes low, it is most likely a
faulty power supply or cable. If the noise persists, then it is likely an inherent fault
with the camera, which might not be easy to resolve.
12.3.1 Flat-Field Noise
Flat-field noise cannot be directly measured, as the noise is the variation in the flatness
of the image frame after the application of the flat field.
The noise in a calibrated frame is given by
σ cal =
σ
2
Bias + σ
2
Dark σ
2
Flat ,
(12.1)
which we can rearrange as
σ Flat =
σ
2
cal − σ
2
Dark − σ
2
Bias .
(12.2)
Hence, we can get to the flat-field noise by measuring the noise in a calibrated
frame. Ideally, you need a calibrated frame that has few stars in the image. The noise
within the frame will have to be measured away from any star or other astronomical
objects in the field, although this is not a problem for dome flats. Again, this may be
achieved by sigma clipping the calibrated frame, or the region function of SAO DS9
can be used to select and analyse a region of the calibrated frame free from stars.
By applying (12.2), we obtain the flat field noise σ Flat . You may wish to use multiple
images and multiple flat-field frames to obtain a more accurate uncertainty reading.
Poorly implemented flats-field frames can be a significant noise contributor. Good
flats take a considerable time to undertake, and if twilight flats are being used, the
area of the sky selected is often suboptimal and may vary in brightness. Although
sky flats are normally considered the best method to obtain flats, improvements in
flat-field lighting sources have closed the gap between sky flats and dome flats.
A typical dome flat is taken using the inside of the dome. This is unlikely to be a
uniformly reflective surface, and the dome lights are unlikely to have a flat spectrum.