(Updated Feb 13) These are the updated estimate of the exposure times needed to get best possible signal for the defocused data. This was done by assuming that

1. The behavior of the flux as a function of the defocus is the same as in December 2017 data - this is verified in the new data
2. Flux levels as a function of the time behaving as seen in the data taken on January 24, January 25 and February 2 (i.e., includes comment by fmadec below from Feb 1).
3. Reduction of flux levels is achieved with attenuator. This is pending other possible solutions suggested by Robert (https://pfspipe.ipmu.jp/jira/browse/PIPE2D-323?focusedCommentId=14830&page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel#comment-14830)  and Jim (put in a filter as well anywhere in the beam?). Attenuator response is estimated in PIPE2D-323.

The recommended exposure times for HgAr (modified by the comment by fmadec below):

In focus: 15 seconds with attenuator at 165
Defocus +-0.5 mm:  15 seconds with attenuator at 110
Defocus +- 1 mm:    20 seconds (no attenuator for this and all other exposures below)
Defocus +- 1.5 mm:   38 seconds
Defocus +- 2 mm:  62 seconds
Defocus +- 2.5 mm:   95 seconds
Defocus +- 3.0 mm:   135 seconds
Defocus +- 3.5 mm:   182 seconds
Defocus +- 4.0 mm:   237 seconds
Defocus +- 4.5 mm:   297 seconds 
 
The recommended exposure times for Neon:

In focus: 15 seconds with attenuator at 210
Defocus +-0.5 mm:  15 seconds with attenuator at 190
Defocus +- 1 mm:    15 seconds 15 seconds with attenuator at 135
Defocus +- 1.5 mm:   15 seconds with attenuator at 65
Defocus +- 2 mm:  18 seconds (no attenuator for this and all other exposures below)
Defocus +- 2.5 mm:   27 seconds
Defocus +- 3.0 mm:   29 seconds
Defocus +- 3.5 mm:   51 seconds
Defocus +- 4.0 mm:   67 seconds
Defocus +- 4.5 mm:   85 seconds 

Note that, in order to reduce the data, we would like all the other calibration images as well (INSTRM-562)  fmadec, please understand that it is not completely trivial for me, from this distance and with limited understanding of the system, to estimate these times so they should be only used as rough guidance and feel free to adjust them if you see obvious problems.

We are interested in most data possible without saturating the detector.
For HgAr, brightest line which would saturate is the Argon line at 912.56 nm, positioned roughly at y=3378 when looking at the raw image and the central fibers on the detector.
For Neon, the line that is to be optimized is at 668.01764 nm, positioned roughly at y=550 when looking at the raw image and the central fibers on the detector.
 
It is not very illuminating, but just in case and for my own purposes, I put the notebook used to estimate these times at: https://github.com/nevencaplar/PFS_Work_In_Progress/blob/master/Other_Notebooks/Flux_Calculation_For_LAM_January_2019.ipynb