| 3 | | || || peak || hwhm || (im*kern)^2 / (var * (kern^2))|| (im*kern)^2 / (var * kern) || |
| | 3 | For this test, I selected a sample of stars over two orders of peak flux levels, and then convolved them with various Gaussian kernels in mana. For all lines below the colors and kernel sizes are: |
| | 4 | |
| | 5 | || color || kernel sigma || |
| | 6 | || red || 0.0 || |
| | 7 | || green || 0.5 || |
| | 8 | || blue || 1.0 || |
| | 9 | || purple|| 2.0 || |
| | 10 | || cyan || 3.0 || |
| | 11 | || brown || 4.0 || |
| | 12 | || yellow|| 5.0 || |
| | 13 | |
| | 14 | I used different kernels for the variance. The first set of plots below use the variance * kern^2^, which is equivalent to convolving with a kernel 1/sqrt(2) times the sigma of image. This is the mathematically correct method. The second set of plots use the variance * kern, where the same kernel is used on the image as is on the variance. This is not the mathematically correct method, but probes the space of "what if we convolve the variance incorrectly". |
| | 15 | |
| | 16 | || || peak || hwhm || (im*kern)^2^ / (var * (kern^2^))|| (im*kern)^2^ / (var * kern) || |
