After reading many different opinions about average stacking in photometry, I have decided to do a test with Maxim DL to undesrstand if the average stack feature offered by the software is a viable option to effectively increase the SNR of stars without detroying the data. I think it can be of interest to post the results. The method that I have used is to do single image photometry using a time series, then calculate the fluxes, then average three fluxes at a time and then got the averaged magnitudes. After that I have used the average stack of Maxim DL to stack the images in groups of three and then compared the resulting magnitudes with the ones gotten with the above-mentioned method. Here are the results:
Time (JD)
Mag
Flux
Average Flux
Average mag
Average stack Maxim DL (3 images)
Delta Mag.
2457242,41222222
-0,0881
1,0845260797
2457242,4137037
-0,0748
1,0713219423
2457242,41518519
-0,0777
1,0741872667
1,0766784296
-0,0802
-0,0800
-0,0002
2457242,41666667
-0,0839
1,0803388649
2457242,41814815
-0,078
1,0744841166
2457242,41962963
-0,078
1,0744841166
1,0764356994
-0,0800
-0,0802
0,0002
2457242,42111111
-0,0801
1,0765643643
2457242,42259259
-0,0836
1,0800403975
2457242,42407407
-0,0798
1,0762669397
1,0776239005
-0,0812
-0,0813
0,0001
2457242,42555556
-0,0801
1,0765643643
2457242,42703704
-0,0805
1,0769610583
2457242,42851852
-0,0816
1,0780527208
1,0771927145
-0,0807
-0,0805
-0,0002
2457242,43
-0,0793
1,0757714145
2457242,43148148
-0,079
1,075474209
2457242,43295139
-0,0917
1,0881280355
1,0797912197
-0,0833
-0,0837
0,0004
2457242,43444444
-0,0785
1,0749790488
2457242,43592593
-0,0834
1,079841465
2457242,43740741
-0,0872
1,0836274553
1,0794826564
-0,0830
-0,0826
-0,0004
2457242,43888889
-0,0882
1,0846259729
2457242,44037037
-0,0853
1,0817328038
2457242,44185185
-0,0765
1,0730006869
1,0797864879
-0,0833
-0,0829
-0,0004
2457242,44333333
-0,0759
1,0724078887
2457242,44481481
-0,0856
1,0820317389
2457242,4462963
-0,0917
1,0881280355
1,0808558877
-0,0844
-0,0847
0,0003
2457242,44777778
-0,0896
1,0860254433
2457242,44925926
-0,0824
1,0788473521
2457242,45074074
-0,0878
1,0842264555
1,0830330837
-0,0866
-0,0870
0,0004
2457242,45222222
-0,0801
1,0765643643
2457242,4537037
-0,0772
1,0736926991
2457242,45518518
-0,0936
1,0900338882
1,0800969839
-0,0837
-0,0837
0,0000
2457242,45665509
-0,0858
1,0822310749
2457242,45813657
-0,0918
1,0882282604
2457242,45962963
-0,0856
1,0820317389
1,0841636914
-0,0877
-0,0882
0,0005
2457242,46111111
-0,088
1,0844261958
2457242,46259259
-0,0877
1,0841265991
2457242,46407407
-0,0837
1,0801398775
1,0828975575
-0,0865
-0,0869
0,0004
2457242,46555556
-0,0785
1,0749790488
2457242,46703704
-0,0809
1,0773578986
2457242,46851852
-0,0921
1,0885289906
1,080288646
-0,0838
-0,0844
0,0006
2457242,47
-0,0762
1,0727042468
2457242,47148148
-0,0893
1,0857254049
2457242,47297454
-0,0839
1,0803388649
1,0795895055
-0,0831
-0,0830
-0,0001
2457242,47445602
-0,0873
1,0837272657
2457242,4759375
-0,0831
1,079543135
2457242,47741898
-0,0918
1,0882282604
1,083832887
-0,0874
-0,0873
-0,0001
2457242,47890046
-0,0872
1,0836274553
2457242,48038194
-0,0894
1,0858254085
2457242,481875
-0,0849
1,0813343521
1,0835957386
-0,0872
-0,0870
-0,0002
2457242,48334491
-0,0884
1,0848257867
2457242,48483796
-0,0904
1,0868259513
2457242,48631944
-0,0894
1,0858254085
1,0858257155
-0,0894
-0,0897
0,0003
2457242,48780093
-0,0871
1,0835276541
2457242,48928241
-0,091
1,0874267195
2457242,49076389
-0,0904
1,0868259513
1,085926775
-0,0895
-0,0893
-0,0002
2457242,49224537
-0,0886
1,0850256374
2457242,49372685
-0,0847
1,0811351813
2457242,49520833
-0,0965
1,0929492591
1,086370026
-0,0899
-0,0901
0,0002
2457242,49668981
-0,095
1,0914403364
2457242,4981713
-0,0915
1,0879276134
2457242,49965278
-0,0989
1,0953678756
1,0915786085
-0,0951
-0,0954
0,0003
2457242,50114583
-0,0921
1,0885289906
2457242,50261574
-0,0994
1,0958724273
2457242,50409722
-0,094
1,0904355455
1,0916123211
-0,0952
-0,0953
0,0001
2457242,50559028
-0,0949
1,0913398157
2457242,50707176
-0,1013
1,0977918443
2457242,50855324
-0,0982
1,0946618934
1,0945978511
-0,0981
-0,0986
0,0005
2457242,51003472
-0,0935
1,089933497
2457242,5115162
-0,0982
1,0946618934
2457242,51300926
-0,1013
1,0977918443
1,0941290782
-0,0977
-0,0977
0,0000
2457242,51449074
-0,0975
1,0939563663
2457242,51597222
-0,0977
1,094157899
2457242,5174537
-0,0881
1,0845260797
1,090880115
-0,0944
-0,0949
0,0005
2457242,51893518
-0,1061
1,1026558858
2457242,52041667
-0,0989
1,0953678756
2457242,52107639
-0,0972
1,0936541367
1,097225966
-0,1007
-0,1003
-0,0004
2457242,52255787
-0,1019
1,0983986741
2457242,52403935
-0,0972
1,0936541367
2457242,52552083
-0,1017
1,0981963603
1,0967497237
-0,1003
-0,1002
-0,0001
2457242,52699074
-0,1045
1,1010321487
2457242,5284838
-0,1007
1,0971853497
2457242,5299537
-0,0979
1,0943594689
1,0975256558
-0,1010
-0,1016
0,0006
2457242,53144676
-0,1027
1,0992083024
2457242,53291667
-0,0988
1,0952669931
2457242,53439815
-0,1
1,0964781961
1,0969844972
-0,1005
-0,1008
0,0003
2457242,5358912
-0,1022
1,0987022148
2457242,53738426
-0,101
1,0974885551
2457242,53886574
-0,1033
1,0998159153
1,0986688951
-0,1022
-0,1024
0,0002
2457242,54034722
-0,0942
1,0906364297
2457242,5418287
-0,0969
1,0933519907
2457242,54331018
-0,1055
1,102046704
1,0953450414
-0,0989
-0,0993
0,0004
The above-mentioned time series was done as a simple ensemble differential photometry, clear filter.
I think I can conclude that the average stack feature of Maxim DL is actually an excellent way to increase the SNR of stars without altering the data as the measures differences are in the order of a few tenths of millimag.
Gianluca (RGN)
Hi Gianluca:
As I would have expected/hoped the stacked (3) magnitude, and the average of three individual magnitudes were the same.
Was the stacked SNR an improvement over the individual SNR and by how much?
Ken
Hi Ken,
the SNR improvement of the 3 stracked images was around 1.7 times better than the single ones as I would expect. The method I have followed was recommended by a professional astronomer who wanted to learn how the software handels the fluxes. Anyway I think it is good to learn that automatic average stacking does not alter the magnitudes you could get by averaging manually.
Gianluca
Gianluca:
Good to hear the SNR improved by sqrt n. I asked because in many of my own tests, the SNR often does not improve by the level expected but quite a bit less due to significant noise.
Ken
Gianluca,
Is there an option in maxim to shift by whole pixels only so the star profile and background are not redistributed among pixels from bicubic or bi-linear resampling in the shifting operation. Full pixel shifting increases the FWHM somewhat but it doesn't redistribute the background. In the program I use you accomplish this by using shifting only for the transformation and Nearest Neighbor for the resampling process:
"Nearest Neighbor: Uses the pixel nearest to the transformed coordinate instead of re-sampling the pixel values. This inflates the FWHM by about 0.3 pixels but preserves the noise structure of the image, which is usually important when Aperture Photometry will be done on the registered images."
The result is that images are only shifted and are shifted only by whole pixel amounts during the alignment process.
Brad Walter, WBY