Report by Drew Phillips, 11 Oct 2001


In March 2001, we concluded that the DEIMOS camera exhibited flexure of approximately 9 x 8 px (full range). This was done using the COHU detector with a light source (rigidly attached beside the COHU) in the focal plane of the camera, and a small mirror mounted in front for the camera. The observed motion was approximately 30 COHU (10-micron px), which gets divided by 2 for the double-pass and adjusted for the change in pixel size to give the image motion quoted. Two likely suspects for this camera flexure were Element 3 and Body 4. This report describes a succesful attempt to identify the source of the DEIMOS camera flexure, using "pinhole shadow tests".

1. Concept of Pinhole Shadow Tests

The basic idea is that rays from a pinhole light source located a short distance in front of the camera will illuminate dust, condensation, optical defects, etc. (hereafter refered to as "dust" features) and cast shadows onto the detector. This will allow us to directly see radial motion of elements within the camera, provided that an appropriate dust feature is located on one the the surfaces of the moving element. Furthermore, since the light rays from the pinhole source will illuminate the camera differently than the collimated light from the spectrograph, we should in principle be able to locate the moving dust feature within the camera. In practice, it's easier to move the pinhole source slightly and use the parallax to precisely locate each dust feature within the camera.

Being able to identify the surfaces that each feature lies on means that the surface(s) where condensation forms can be identified as well.

Another use for these tests is to measure detector motion. Dust features on the Dewar window, being far from the pinhole source and near the detector, should appear fixed. Any motion of these features is attributable to the detector moving underneath the Dewar window, so that flexure in the detector mounting can be immediately infered.

A final use, not envisioned originally, involves a large motion of the pinhole source (or a "double-pinhole" source, as was the case). The parallax allows us to precisely determine the distance of the mosaic behind the Dewar window.

2. The Camera Model

While much of the analysis could be analytical using geomtrical optics, in practice it was much easier to use a computer model of the camera and perform ray traces. This model was based on the ZEMAX model description of the 22C camera supplied by ORA. Its primary simplification is that it does not include any aspheric surfaces, but since our analysis applies to differential measurements, this should be quite adequate. The model includes 22 refractive surfaces (each characterized by an (x,y,z) location of the vertex, a radius of curvature, a thickness and an index of refraction) plus the CCD surface. The output showed the position and direction vectors for the intersection at each surface; inputs include the postion of the pinhole and angle of the test ray. In use, the angle was characterized by a single value (r1) which corresponds to the sine of the ray angle with respect to the optical axis.
Example:   dcam delx=0 r2=0 r1=0.02 (pinhole on-axis, angle=1.15 deg):
(Surf      Xmm       Ymm      Zmm               r1         r2        r3)
 1:x:    1.0002    0.0000   50.0008;     r:  0.011481  0.000000  0.999934
 2:x:    1.1446    0.0000   62.5751;     r:  0.014115  0.000000  0.999900
 3:x:    1.1458    0.0000   62.6615;     r:  0.013784  0.000000  0.999905
 4:x:    2.0225    0.0000  126.2587;     r:  0.018804  0.000000  0.999823
 5:x:    4.5123    0.0000  258.6449;     r:  0.012204  0.000000  0.999926
 6:x:    5.4730    0.0000  337.3590;     r:  0.010430  0.000000  0.999946
 7:x:    5.4997    0.0000  339.9119;     r: -0.000301  0.000000  1.000000
 8:x:    5.4968    0.0000  349.5611;     r:  0.004617  0.000000  0.999989
 9:x:    5.4981    0.0000  349.8421;     r:  0.003869  0.000000  0.999993
10:x:    5.8717    0.0000  446.3934;     r:  0.004120  0.000000  0.999992
11:x:    5.8720    0.0000  446.4772;     r:  0.002738  0.000000  0.999996
12:x:    5.8983    0.0000  456.0860;     r:  0.015955  0.000000  0.999873
13:x:    6.4463    0.0000  490.4279;     r:  0.001863  0.000000  0.999998
14:x:    6.4637    0.0000  499.7328;     r:  0.007672  0.000000  0.999971
15:x:    6.4643    0.0000  499.8218;     r:  0.004824  0.000000  0.999988
16:x:    6.9268    0.0000  595.7017;     r: -0.000585  0.000000  1.000000
17:x:    6.8897    0.0000  659.1201;     r: -0.000585  0.000000  1.000000
18:x:    6.8862    0.0000  665.1191;     r: -0.000585  0.000000  1.000000
19:x:    6.8714    0.0000  690.3928;     r:  0.014141 -0.000000  0.999900
20:x:    6.9105    0.0000  693.1544;     r:  0.033133 -0.000000  0.999451
21:x:    7.1279    0.0000  699.7109;     r:  0.022712 -0.000000  0.999742
22:x:    7.4164    0.0000  712.4106;     r:  0.033133 -0.000000  0.999451
IM x:    7.6388    0.0000  719.1210;     r:  0.033133 -0.000000  0.999451

Thus, the ray falls at (x,y) = (7.64,0)mm on the CCD.

In the model, the pinhole was typically set 50mm in front of the first element (close to actual location) but the tests tend to be very insensitive to the exact distance. (The pinhole distance is actually at 0, with the first lens element at 50mm, as seen in the example above.)

Two tests were performed to verify the model. This first was simply to see if the plate scale was reasonable. The second was to see if on-axis collimated light was brought to a reasonable focus. This test required modelling an actual 6mm filter (assumed index = 1.545) and was run for 2 cases: a Back Focal Distance (BFD) of 0.2642in (Model B) and 0.287in (Model C).

 Radius at       Radius at       Radius at
 entrance        detector        detector
                  (Mod.B)         (Mod.C)
  .5mm            0.04 px        -0.01 px
   1mm            0.08 px        -0.03 px
   2mm            0.15 px        -0.05 px
   4mm            0.29 px        -0.12 px
   6mm            0.38 px        -0.23 px
   8mm            0.41 px        -0.39 px
  10mm            0.37 px        -0.63 px
  12mm            0.24 px        -0.97 px
  14mm           -0.01 px
  16mm           -0.41 px
  18mm           -0.95 px
  20mm           -1.67 px
Model C is near the BFD predicted by the 22C ORA model. Model B gives a somewhat better focus across a larger-diameter input beam. The obvious spherical aberration is no doubt due to the exclusion of aspheric terms in the model. Nevertheless, Model B manages to focus a 32mm diam input beam into less than 1 pixel.

Typical use: for most of the analysis, the model was used on- or near-on-axis. For example, the on-axis case produces a spot at (0,0)mm. Then an element would be displaced by 0.1mm, and the on-axis input ray traced again, yielding the amount of image motion at the detector. Finally, r1 would be adjusted so that the ray passed through x=0.1mm at the lens surface; this would yield the amount of shadow motion. For a few special cases, the model was run to produce results at a specific location on the detector.

3. The Double Pinhole Test, Sept. 12 (Figure)

In the initial attempt to perform this test, the calibrated pinhole (5 micron diam.) was held in place by two nylon screws, 18.8 mm apart; it was not foreseen that the nylon would transmit light from the light source behind. Thus, these images are dominated by light from 2 rather diffuse sources 18.8mm apart. The images show a few very sharp features, many fairly sharp features (including the central condensation patch), and some very blurry images. Analysis (see section 3B) place the blurry features on the field-flattener and on the window-glass filter which was in place during these initial tests. Features in the images are generally "doubled" with spacing of 53-54px for the numerous "fairly-sharp" features and 23px for the less common "very-sharp" features (typical diameters of 12 and 17px, respectively). The lower portion of the image is darker and only shows one set of images, consistent with one of the light sources being occulted. [The pinhole light source is held on the "camera mirror" spider, and the occulting object is the mirror itself, located slightly to the side about 1 inch in front of the pinhole.]

We have identified the following features with different separations:

  Feature:                  Obs. separation (pix)
  1. Very sharp rings             23
  2. Frost &c, sharp rings       53-54
  3. Dark rings                  84-94
  4. Dark blobs                   204
  5. Diffuse rings                468
Since only features very near the detector are usable, these data are not useful for studying camera flexure. However, they may be used for three ancillary studies: location of condensation, distance to CCD, and detector motion.

A. Location of Condensation:

There are two likely spots for condensation to form: on the front of the Dewar window, and on the front of the field flattener (Element 9). Note that the space between Element 9 and the window is small and semi-sealed, and that Element 9 is in thermal contact with the window at the edges. The back of Element 9 is an unlikely location, since moisture will condense onto the Dewar window instead. The front of Element 9 has been the expected location, since the growth of condesation over time, and the current amount of condensation, clearly requires a volume of air greater than the space between Element 9 and the Dewar window.

On-axis results from Model A (which uses the 0C design camera, as the ORA 22C model had not been received) state that dust/etc. on the front of the Dewar window should cast shadows separated by 49px, while those on the back of the window should cast shadows separated by 18px. This is close to the 53-54px measured for the "[fairly-]sharp rings" and 23px measured for the "very-sharp rings". Since the features are located so close to the detector, this prediction is largely insensitive to the pinhole distance in front of the camera, but it will be affected by the assumed distance to the CCD (see next section). Also, note that there are no features seen with separations less than 54 and 23 pixels, arguing that these will be the 2 surfaces closest to the CCD.

The appearance of the condensation is that of "frost" at the edges of the patch, and "ice" toward the center (as evidenced by linear light cusps). There is also an obvious water droplet, whose edge casts images separated by 54 px. This argues that the condensation consists of both liquid water and ice. See images of temporal changes also.

Thus we conclude that the bulk of the condensation is on the front of the Dewar window. We cannot rule out some condensation in the center of Element 9, since the condensation patch at the center of the window is so large, but there is no direct evidence for it.

B. Distance to CCD:

The lack of a truly close match in the results of the model above (Model A) argues that the Back Focal Distance (BFD) is incorrect. Thus, we can adjust the BFD to find a closer match. Model D (which incorporates as closely as possible the exact setup used, including a filter), gives the closest match at 54.2 and 22.7px for the front and back, respectively. This model puts the CCD at a distance of 6.41mm (0.2524in) behind the Dewar window. With potential measurement errors of 0.5px in each, the error in distance is +/- 0.4mm.

One frame (4243) was also taken at the back of the focus travel. Quick measurements of the image separations on this image are 62 and 29 px. This corresponds to a BFD of about 8.21mm +/- 0.4mm (0.3232in). Also, a more sensitive test for the range of the focus stage (using the change in plate scale across more than half the detector) yields a range of 1.9mm, very close to the expected value.

The expected CCD distance, according to measurements provided by Terry Pfister, is 0.2738in +/- 0.040in, or 5.94 to 7.97mm, behind the Dewar window. These pinhole measurements indicate we are behind that range by about 0.4mm.

An aside:

With Model D, we get a good match for all surfaces between the back of Body 4 and the detector, as follows:

   Feature:            Obs.sep.(pix)     Mod.D (on-axis)    Surface
  1. Very sharp rings      23              22.7           Back Dewar Win.
  2. Frost &c, sharp rings 53-54           54.2           Front Dewar Win
  3. Dark rings           84-94 (off axis) 80/86 on-axis  Bk/Front Elem9*
  4. Dark blobs           204             189/205         Bk/Frt Filter
  5. Diffuse rings        468              459            Back Elem 8

(*) Elem 9 is steeply curved, so image separation depends on both surface
(back/front) AND distance off-axis.

C. Detector Motion

We can use the apparent motion of the features on the Dewar window to measure the flexure of the detector mosaic as DEIMOS is rotated. The measurements were done by selecting some strong features, building an averaged template, and cross-correlating. Results are that the detector flexes in the direction of gravity by 1.8px (X) and 1.25px (Y). The motion is very well behaved and there is only negligible hysteresis. [NB -- flexure quoted is radius, thus full range of flexure is 3.8 x 2.5 px]

(After the camera flexure was identified (Section 4), a small correction for the changing angle of the rays striking the CCD means that the mosaic flexure should be slightly larger, by 0.14px, than determined here.)

4. Camera Flexure Studies (Sept. 13, with followup Oct. 03)

Data collected on Sept. 13 had the nylon screws replaced with steel screws, and a 100-micron pinhole in place. A full rotation sequence was obtained. On Oct. 03, the pinhole was shifted slightly, to allow parallax measurements to determine the exact location of features in the camera.

To determine strongly moving features, images at different rotations were "blinked" against each other; a few features were found that showed large motions. (It was later found that dividing the images was a quicker way to locate these features.) Three "spots" (rings), labelled A, B and C, were strong enough to measure. Subsections around these spots were extracted and shifted to remove the mosaic motion (that is, features on the Dewar window were made stationary). Smaller subsections around each spot were extracted, shifted and combined to form a template for each spot; the template was also rotated 180 degrees so that cross-correlation would not pick up any residual background features. Templates were then cross-correlated against the individual images in order to measure motions.

Within each of the subsections above, it was noticed that the relatively-common "diffuse rings" also had a slight motion. Therefore, a region with several prominent "diffuse rings" was treated in a similar manner to measure these motions. These features had been identified with the back of Body 4 (Element 8), an identification confirmed below.

A. Location of Features

On Oct. 03, a pair of images was obtained with the pinhole slightly shifted (with respect to the camera axis) between the exposures. The shift was expected to be 1mm, but due to an error it was only a fraction of this. Nevertheless, the data are usable (and the shift soluable). The table below is separated into two parts -- the first is for on-axis parallax motion, assuming a shift in the light source of 0.32mm, whereas the second is a solution at the location of each of the measured features, with an adjusted value for the pinhole shift of 0.30mm:
SURFACE		MODEL; .32mm	OBSERVED shifts		Feature observed
Front Dewar:	  0.9 px	 < 1 px +/- <<1 px	ice in center
Surface 16:	  8.0 px	 6.7 px +/- 0.5 px	diffuse rings near SpotA
Elem 5/6:	 16.6 px	15.5 px +/- 0.5 px	Spot A ("moving spot")
Front Elem 3:    31.6 px	29.6 px +/- <1 px	Spot B ("moving spot")
Front of cam:	163   px	157. px +/- 2-3 px	Huge Spots F

		at feature
S16 near SPOT A:  6.8 px	 6.7 px +/- 0.5 px
SPOT A:		 15.6 px	15.5 px +/- 0.5 px
SPOT B:		 29.7 px	29.6 px +/- <1 px
SPOTS F:	154   px	157. px +/- 2-3 px
The agreement with specific features is remarkable.

B. Motion of Features and Moving Elements (IMAGES)

As noted above, motion of different components was measured using cross-correlation techniques. Next, the effect of displacing each element was studied using the model, giving us the shadow motion produced by a given offset, and the ratio of shadow motion to image motion. By this technique, we can turn the shadow motion observed here into image motion and determine how much a given element is displaced radially.

1. Diffuse Rings (Back of Body 4)

Description: tilted oval; 3.9 x 3.0 px (X x Y, FULL RANGE); some hysteresis (perhaps 20-40 deg).

Body 4 is a POSITIVE doublet. Image motion will track element motion. Y flexure should be maximum at PA=90; X should be maximum at PA=0 if Body is moving under gravity. This is observed. However, the optical model indicates a shadow/image motion ratio of 3.4 ie, if Body 4 is moving, it is only contributing about 1px of flexure (FULL RANGE). The observed shadow motion implies about +/- 0.8 thou radial offset in Body 4.

2. Spots A and C

Oval helical pattern, closing with reverse rotation, dim 20x19 px; hysteresis about 45 deg.

Oval helical, opening with reverse rotation, dim 18x14 px.

SPOTS A+C have similar size, appearance and (qualitatively) motion. While XA-XC closes and reopens by 10px going from 180 to -180 to 180 again, and YA-YC has similar results (by flipped in sign) the distance between these spots is constant to within about +/- 1 px. Thus, this motion may well be a rotation of Element 5. (del-y/del-x) varies from 1.296 to 1.304, a difference of 0.17 deg. Therefore, Element 5 may be floating and shifting by fairly large amounts, BUT the camera is insensitive to this motion -- the ratio of shadow to image motion is 32:1. The observed shadow motion implies a radial offset of +/- 4 thou.

Note that these spots may be due to bubbles in the coupling fluid (a conclusion supported by the "soft" nature of their motion). However, the phases indicate they follow gravity, which sounds contrary to what bubbles would be expected to do.

The interpretation of these spots is uncertain, and we consider this flexure term questionable.

3. Spot B

This loop closes, but is triangular in shape. There is about 45 deg hysteresis. Dimensions are 19x20, full range.

This spot is associated with the front of Element 3. The ratio of shadow to image motion is 4.4:1, so that this motion is the dominant contribution to camera flexure (4-5 px full range). The triangular shape is consistent with the trifold symmetry of the elements supports. Observed shadow motion implies a radial offset of +/- 2.7 thou.

C. Camera Flexure Summary

We have identified motion associated with 3 optical elements: In addition, we see motion of the mosaic by +/- 1.8 pixels (30% less in Y)

NB: The spots associated with Elem 5 are likely to be bubbles in the fluid couplant, and therefore may not represent actual element motion!!

Summary of motion:

Elem 3:  +/- 2.7 thou ==> +/- 2.3 px image motion
Elem 5:  +/- 4   thou ==> +/- 0.3 px   (??) (somewhat less in Y)
Body 4:  +/- 0.8 thou ==> +/- 0.6 px   (25% less in Y)

Total:                    +/- 3.2 px

Detector (subtracts)      +/- 1.8 px   (30% less in Y)
                          +/- 1.4 px  Total image motion, Camera+detector
Note that the total flexure in the camera derived from shadow motions is +/- 3.2 px, not quite the level of +/- 4.5 px expected from the COHU observations. The difference between the two is not understood. (Possibly there were some flexure in the COHU test setup?)

5. Miscellaneous Items

A. Possible Secondary Effects and Uncertainties

1. The lens motions were worked out on a one-by-one basis and assumed to add linearly. The assumption was verified by applying all of the motions simultaneously in the model; the same net result was obtained.

2. Since we have a filter in place during normal operation, there is the possibility that the presence of a filter might affect the shadow:image motion ratios. Therefore, a set of model runs were made with the filter in place and moving the elements radially as before. The ratios changed negligibly:

     Elem    Surfaces      Ratio w/o filt      Ratio w/ filt
       3        5/6             4.38                4.41
       5        9/10           32                  32
      7+8      13/16            3.37                3.42

3. The distance from the pinhole light source to the camera was estimated to be 50mm, but was never measured precisely. The derived motion most affected by this uncertainty would be that of Element 3, which is closest to the light source. We thus derived the ratio of shadow:image motion using a distance of 40mm instead; the ratio changed from 4.38 to 4.52. Since a 20% change in distance produced only a 3% change in estimated image motion, we conclude that this uncertainty is not very significant.

B. Distortion (Differential Flexure)

Displacing the camera elements as above produces slightly different image motion across the image. With rays originating at the pupil (11.5in in front of camera) we find:

        r1     Theta   Del-x_(mm)  rel_to_0.0551mm
      -0.16     -9.2     0.0550        0.0001
      -0.14     -8.0     0.0529        0.0022
      -0.12     -6.9     0.0510        0.0041
      -0.10     -5.7     0.0495        0.0056
      -0.08     -4.6     0.0485        0.0066
      -0.06     -3.4     0.0475        0.0076
      -0.04     -2.3     0.0470        0.0081
      -0.02     -1.1     0.0467        0.0084
       0	 0       0.0466        0.0085
       0.02      1.1     0.0466        0.0085
       0.04      2.3     0.0470        0.0081
       0.06      3.4     0.0476        0.0075
       0.08      4.6     0.0484        0.0067
       0.10      5.7     0.0497        0.0054
       0.12      6.9     0.0509        0.0042
       0.14      8.0     0.0529        0.0022
       0.16      9.2     0.0553       -0.0002
Thus, we see that with flexure compensation at the edges of the mosaic, the camera flexure would still produce an image motion of +/- 0.0085mm or +/- 0.57px at the center of the detector. Failure to fix the camera flexure would thus degrade image quality.

In November 2000, we had identified 0.5px full range differential flexure between points near +/- 54mm and points near +/- 6.6mm on the mosaic, corresponding to r1 of 0.138 and 0.018, respectively. Predicted flexure over this range would be +/- 0.40px (at r2=0.0393, appropriate for these observations), larger than what was seen by nearly a factor of 2. However, the camera flexure may well have worsened over the past year if it is due to a shim slipping as is hypothesized.

C. Image Motion Caused by Filter

Most of the data collected on Sept. 13 had the filter removed from the optical train, but the final exposure (4320) had the science filter inserted for direct comparison with the previous frame (4319). It was found that images of features in front of the filter shifted by about 7 pixels toward lower X (image coordinates). This raised the issue of whether the filter might be contributing to flexure. However, subsequent tests using the FCS and applying pressure to the filter wheel in various directions did not produce any image motion, so it seems likely that the observed shift in images is due to wedge in the filter.

Last modified: 11 oct 2001

Andrew C. Phillips / Lick Observatory