In order to better understand the various data-reduction methods, I test here a modified forward model. It consists of a test on synthetic images – this allows us to test what the error is relative to the ‘truth image’.
A synthetic ‘observed image’ is generated as the convolution of an ideal image with Poisson noise and an intensity offset as in a pedestal. This pedestal models the effect of small error sin bias subtraction.
Trial images are next generated and compared to the observed image – when a good match is found the winner model image is declared. We estimate errors in a box on the DS. We use a grid search in alfa for the PSF and in offsets. We CALCULATE a factor that scales the intensity so that once the offset and the PSF are chosen the resulting image is scaled so that the total flux is the same as in the observed image.
We used 0 bias or offset and we used 0.01 as the offset. We used alfa =1.6, 1.7 and 1.8. We allowed loops that bracketed these values.
The test was based on the RMSE between the observed image and the trial images. For the winning model image the error between the known ideal image intensity inside the box and the intensity inside the same box in the offset and scaled (but unconvoluted) image was calculated.
We found errors in the 0.0 to 0.75% range, seemingly independent of the value of alfa or offset.
The above was for one lunar phase near new Moon. We repeated the test on an image with a phase larger (like quarter moon). We found errors from 0 yo 1.85% with a tendency to be large for small alfa – i.e. broad PSFs.
The above shoul dbe repeated for all phases.
The results are similar to what we have found for the EFM method – but for that method results are available for all phases, so – … (more later)
On the above we note that the best solution found seemed to have biases in the alfas and the offset – nevertheless the best solution was fairly good, as shown.
So: the above test was witha method that unlike the EFM did not constrain the trial images to ‘fit through the sky’, but it did, like the EFM, constrain the total flux.