Happy Fourth of July!

The following is a brief overview of how we are analyzing the wavefront aberration and includes the aberration parameters calculated for 9 different temperature differences. So far we are still seeing the cylindrical power even after removing the tape/glue on the Hartmann plate. Attached are the relevant matlab codes and a couple of plots of the wavefront aberration.

We took pictures when the camera was in equilibrium at room temperature and then at each degree increase in camera temperature as we heated the room using the air conditioner. For each degree increase in camera temperature, we compared the spot positions at the increased temperature to the spot positions at room temperature. We used the following codes to generate the aberration parameters and make plots of the wavefront aberration:

-build_M.m (builds 8 by 8 matrix M from centroid displacements)
-wf_aberration_temperature_bygrid.m (main script)
-wf_from_parms.m (generates 2D aberration array from aberation parameters)
-intgrad2.m (generates 2D aberration array from an interpolated array of centroid displacements)

In order to perform the "inverse gradient" method to obtain contours, we first interpolated the centroid displacement vectors to generate a square array. As this array has some NaN (not a number) values, we cropped out some outer region of the array and used array values from (200,200) to (800,800). Sorry we forgot to put that part of the code in wf_aberration_temperature_bygrid.m.

The main script wf_aberration_temperature_bygrid.m needs to be revised so that the sign conventions are less confusing... We will update the code later.

The initial and final temperature values are as follows:

Aberration parameters:

1) Comparing high temp (+10)  with room temp

        p: 1.888906773203923e-004
       al: -0.295042766811686
      phi: 0.195737681653530
        c: -0.001591869846958
        s: -0.003826146141562
        b: 0.098283157674967
       be: -0.376038636781319
        a: 5.967617809296910

2) Comparing +9 with room temp

        p: 1.629083055002727e-004
       al: -0.222506109890745
      phi: 0.193334452094940
        c: -0.001548838746542
        s: -0.003404217451916
        b: 0.091368295953142
       be: -0.351830698303612
        a: 5.764068008962653

3) Comparing +8 with room temp

        p: 1.485283322069376e-004
       al: -0.212605187544093
      phi: 0.206716196097728
        c: -0.001425962488852
        s: -0.003148796701331
        b: 0.089936286297599
       be: -0.363538909377296
        a: 5.546514425485094

4) Comparing +7 with room temp

        p: 1.284124028380585e-004
       al: -0.163672705473379
      phi: 0.229219952949728
        c: -0.001452457146947
        s: -0.002807207555944
        b: 0.084090100490331
       be: -0.379195428095102
        a: 5.289173743478881

5) Comparing +6 with room temp

        p: 1.141756950753851e-004
       al: -0.149439038317734
      phi: 0.240503450300707
        c: -0.001350015836130
        s: -0.002529240946848
        b: 0.078118977034120
       be: -0.326704416216547
        a: 4.847406652448727

6) Comparing +5 with room temp

        p: 8.833496828581757e-005
       al: -0.071871278822766
      phi: 0.263210114512376
        c: -0.001257787180513
        s: -0.002095618522105
        b: 0.069587080420443
       be: -0.335912998511077
        a: 4.542557551218057

7) Comparing +4 with room temp

        p: 6.217428324604411e-005
       al: 0.019965235199575
      phi: 0.250991433584904
        c: -0.001266061216964
        s: -0.001568527823273
        b: 0.058323732750548
       be: -0.289315790283207
        a: 3.957825468583509

8) Comparing +3 with room temp

        p: 4.781068895714900e-005
       al: 0.140720713391208
      phi: 0.270865276786418
        c: -0.001228146894728
        s: -0.001371110045136
        b: 0.052794990899554
       be: -0.273968130963666
        a: 3.591187350052610

9) Comparing +2 with room temp

        p: 2.491163442408281e-005
       al: 0.495136135872766
      phi: 0.220727346409557
        c: -9.897729773516012e-004
        s: -0.001076008621974
        b: 0.048467660428427
       be: -0.280879088681660
        a: 3.315430577872808

10) Comparing +1 with room temp

       p: 8.160828332639811e-006
      al: 1.368853902659128
     phi: 0.116300954280238
       c: -6.149390553733007e-004
       s: -3.621216621887707e-004
       b: 0.025454969698557
      be: -0.242584267252882
       a: 1.809039775332749

The first plot is of the wavefront aberration obtained by integrating the gradient of the aberration and the second plot fits the aberration according to the aberration parameters so is smoother since it is an approximation.