Scatter light Measurements on APO 3.5-m After Installation of M2 & M3 Baffles

 

Jeff Morgan

UW Astronomy

January 2004

 

The Motivation Behind This Study

This is a report on scattered light measurements on the APO 3.5-m telescope after two-thirds of the intended baffling has been installed.  For the purposes of verifying the design of the proposed NA2 baffle, we would very much like to know where the current sources of scattered light are coming from in the telescope.  The primary function of the NA2 baffle will be to limit the detector’s view of the inside of the NA2 tunnel and its view of the M3 cap.  We would like to know if the current NA2 baffle design will be sufficient to exclude the scattered light sources, which we are currently seeing.

 

A Description of the Data

The measurements taken for this report consisted of a series of deep sky images while the moon was at nearly full phase. I would like to thank Jack Dembicky for the capable acquisition of the data used here.  Some clouds were present during the night that these data were acquired, but the images of the scattered moonlight appear to be self-consistent, so it is not thought that the sporadic cloud cover had a significant impact on this data set.  All of the data seen here were taken with SPIcam using 2x2 binning on the night of November 10, 2003.

 

The moon was centered in the slit enclosure and the telescope was tracked at the lunar rate during these exposures.  The exposure times for each of the images varied according to their distance to the moon and ranged from 1 second to 180 seconds.  The total angular range covered in the measurements was from –8 to +32 degrees, where positive degrees refer to directions at higher altitudes than that of the moon.  There were some data acquired with offsets perpendicular to the enclosure slit direction, but not enough to be of interest in this report.  With all of the data shown here, the offsets from the moon refer to offset directions along the enclosure slit.  The offsets from the moon were taken in multiples of two (2, 4, 8, 16, and 32 degrees) on both sides of the moon.  The offsets in the negative direction were limited by the proximity of the horizon.  Typically, several sky images were taken at each offset.  A log of the observations used in this report is given in Table 1.  The numbers in the comment section are the average intensities in each raw image averaged with the IRAF routine imstat over the central area defined by the coordinates [500:550,500:550].  The standard deviations for these averages are also given.   The notation L,R,T,& B refers to left, right, top, and bottom, respectively.

 

 

Table 1.  List of Observations. All images were taken through V filter with 2x2 binning. Directory: /export/images/EN031111/

Image Filename	Altitude Offset	Azimuth Offset	Exposure Time	Comments (imstat [500:550,500:550])
scatter.0001	+2	0	10s	9395+-79
scatter.0002	+4	0	30s	6627+-58, perfect, used for “flat”
scatter.0003	+8	0	60s	25343+-170,(clouds), perfect
scatter.0004	+8	0	60s	7101+-65, some shadowing L&R
scatter.0005	+16	0	60s	3333+-40, L&R shadow, ~10%
scatter.0006	+16	0	120s	6981+-61, L&R shadow, ~10%
scatter.0007	+32	0	180s	8964+-73, L&T shad., ~20%
scatter.0008	+32	0	180s	9441+-78, L&T shad., ~20%
scatter.0009	-2	0	10s	11266+-90, perfect (~10% B)
scatter.0010	-2	0	10s	11645+-92, perfect (   "  )
scatter.0011	-4	0	30s	10806+-85, perfect (   "  )
scatter.0012	-4	0	30s	10777+-84, perfect (   "  )
scatter.0013	-8	0	60s	15042+-118,(clouds),perfect?
scatter.0014	0	-2	10s	saturated (clouds)
scatter.0015	0	-2	1s	1361+-22, perfect
scatter.0016	0	-2	10s	13686+-104,perfect (R shad.?)
scatter.0017	2	-2	10s	5250+-52,perfect (R shad., 2%?)
scatter.0018	2	-2	20s	10753+-85,perfect (R shad.?)
scatter.0019	4	-2	30s	6902+-59,perfect (L&R shad, 1%?)
scatter.0020	4	-2	45s	9968+-79,perfect (R shad, 2%)
scatter.0021	8	-2	60s	8566+-72, L&R shad, ~3%
scatter.0022	8	-2	60s	8897+-73, L&R shad, ~3%
scatter.0023	16	-2	120s	9732+-78, L&R shad, ~8%
scatter.0024	16	-2	120s	8793+-74, L&R shad, ~8%
scatter.0025	32	-2	180s	9531+-75, L&T shad, ~20%
scatter.0026	32	-2	180s	9191+-78, L&T shad, ~20%
scatter.0027	0	-4	30s	10356+-81, R shad, ~2%
scatter.0028	0	0	1s	saturated -- good!
scatter.0029	0	0	0s	bias
scatter.0030	2	-4	45s	saturated (clouds)

 

The rotator was set at 0 degrees horizon for the observations shown in Table 1.  This means that the horizon remains fixed to the x-axis of the CCD (which is the direction along a row in the image).  The “horizon” direction coincides with the direction of azimuth motion.  Under these conditions the detector’s x-axis remains parallel to the axis that runs between the primary and secondary mirrors.  In other words, with this setting the detector’s x axis remains pointing toward the primary mirror at all telescope orientations and the detector orientation stays fixed with respect to the telescope structures in the primary mirror cell. 

 

Unfortunately, no flat fields are available for these observations.  Instead, one image from the suite of scattered light images must be used as a “standard” flat field.  All of the other images are then divided by this standard image and then renormalized to their original average ADU intensities using the IRAF ccdproc routines.  One must be a little careful in the choice of the image to use for the “standard” flat field. 

 

By measuring the average data in each flat at the different angular distances from the moon you can estimate the local gradient in the lunar scattered light field.  These gradients can then be scaled to SPIcam’s field of view to get an estimate of what one would expect to see for gradients in the moon glow.  Doing this leads to the conclusion that one would expect to see a gradient of about 4% from top to bottom in the SPIcam FOV for images taken +2 degrees of the moon.  These measurements also lead to the conclusion that for observations at greater distances, the gradient in the moon glow is negligible over SPIcam’s FOV.  Inspection of raw images taken at +2 degrees shows no gradients from left to right and a 9% gradient top to bottom that is superimposed on the slight vignetting pattern seen in all SPIcam images. This is in qualitative agreement with the moon glow gradient one expects based on the average counts in each image.  There is an apparent quantitative disagreement between the gradients seen in the raw image and those expected from moon glow. There are several reasonable explanations that could account for this discrepancy, but we will show below that this discrepancy goes away once the flat field corrections are made.  These measurements do confirm that one does not want to use the images within 2 degrees of the moon for the standard flat field.  We have instead chosen one of the +4 degree images (scatter.0002.fits) for the standard flat field for all of the data shown below.  This image was chosen as a good compromise between signal to noise, lack of intrinsic moon glow gradients, and least number of star trails.

 

Under ideal circumstances for flat corrected data you would expect to see a uniform flat response in the sky brightness at all telescope orientations.  But when observing with the APO 3.5-m in the presence of lots of scattered moonlight this ideal is rarely achieved even with the installation of both the M2 and M3 baffles.

 

 

Figures 1 and 2 show data from one of the images taken 2 degrees from the moon.  Each of these figures represents an average of 100 rows or columns.  Figure 1 shows the averaged rows.  The maximum peak-to-peak variation in the image is about 1% of the signal level.  Figure 2 shows the averaged columns from this same image.  The gradient observed in the column dimension is exactly what one would expect from the radial gradient of scattered moonlight at a distance of 2 degrees from the moon.  It appears from this result that the apparent 9% gradient that was present in the raw image was only partially caused by a radial gradient in the moonlight.  After flat field corrections, the difference between the observed and expected gradients disappears.  It would appear then that for at least this image, the applied flat field correction approaches perfection.  But that is not generally found to be the case.

 

Figure 1.  The average of 100 rows from a sky image taken 2 degrees from the moon.  The maximum variation seen is 1%. The image chosen to represent the instrumental flat field was one taken 4 degrees from the moon.

 

Figure 2.  The average of 100 columns from the same image as Figure 1.  An edge-to-edge gradient of 4.6% is seen in this image.  The horizontal line drawn on the graph is only an aid to emphasize the small gradient present in the data.  This gradient is exactly what one would expect for the radial intensity gradient from the moon at 2 degrees distance based on average counts in images at different radial positions.

 

Figures 3 and 4 show data from an image taken 16 degrees from the moon.  Clear errors in the flat field correction are now obvious in both row and column averages.  The left, top, and right sides of these images show decreased scattered light contributions relative to the image that was chosen to represent the standard flat field.  These flat field non-uniformities therefore represent shadowing in the image that was not present in the selected flat field.  Figure 3 shows an average of 100 rows through the middle of the image.  Six and three percent deviations are seen at the left and right edges of the image.  The middle section of the image is quite flat and arrows show the approximate locations where the errors in the flat field become significant.  The row and columns where the shadowing starts to occur are constant across the image.  The shadows seen are essentially linear features across the entire image.  The images taken at +8 degrees from the moon are very similar to what is seen here, with simply smaller deviations and slightly different breakpoints.  The +8 degree images show only 1 and 2 % deviations in the row averages on the left and right sides of the image, respectively.  The flat middle section for the +8 degree images is seen between columns 275 and 835.

Figure 3.  An intermediate case of flat-field non-uniformities.  An average of 100 rows is shown. The middle section of the image is quite uniform, but there are breaks near columns 350 and 875 where shadowing becomes apparent.  The column number where these breaks occur is constant across the image.  The maximum deviation of about 6% was at the far left of the image.

 

Figure 4.  An average of 100 columns is shown from the center of the same image as the data Figure 3.  The 3 peaks below row 400 are from star trails in this image.  The data depart from a perfect flat field correction by 6 % at the top of the image where shadowing appears.

 

The most extreme departures from uniformity are found in images taken the farthest away from the moon.  This is not too surprising considering the fact that the “flat” that they were corrected with was taken at +4 degrees from the moon.  The departures at +32 degrees reach as high as 23 %.  The shadowing observed is similar in morphology to that seen at intermediate distances.  The disappearance of the shadowing on the right side of the image and the depth of the shadowing are the only significant differences from images taken closer to the moon. Figures 5 and 6 and the image shown in Figure 7 illustrate these points.

Figure 5.  This row plot represents the most extreme case of flat field non-uniformities seen since the M2 & M3 baffles have been installed.  It is from the sky image taken at the largest distance from the moon.  The image these data are taken from are shown in Figure 7.  Notice that the point at which the non-uniformities set in has moved up to column 380, the maximum departure at the left side of the image is now ~20 %, and the right hand side of the image is nearly free from the non-uniformities seen here at smaller angular distances to the moon.   The two low data points near column 1000 are the result of a bad column in the chip.

 

Figure 6.  An average of 50 columns from the same image as the data shown in Figures 5 & 7.  Only 50 columns were averaged here owing to the large number of star trails in this image.  Shadowing of ~23 % is seen at the top of the image.  The peak seen near row 800 is from a star trail.

 

Figure 7.  Scattered light image scatter.0008.fits after flat field corrections have been applied.  Star trails are the result of the telescope being set to lunar track rates and the long integration time for the exposure.  The data shown in Figures 5 and 6 were taken from this image.  Shadowing of ~20 % is seen at the left and top of this image.  The black columns to the left and right of the figure are the over- and under-scan regions of the CCD.

 

 

An Interpretation of the Data

 

The first question that needs to be addressed is where does the current shadowing come from?  The shadows observed are straight across the detector and have fairly fast transitions between shadowed and clear portions on the detector.  The further away from the telescope focal plane that a surface gets, the harder it gets for that surface to create a sharp transition on the detector.  In addition, most of the apertures in the telescope itself are curved and circular.  This makes it difficult for them to create perpendicular regions of shadowing that would more likely come from flat, straight, and perpendicular regions in the field of view.  The only places in the optical path where such surfaces reside are in the filter wheel box, which is in SPIcam itself.  Figures 8, 9, and 10 show the physical configuration of the SPIcam dewar and the SPIcam filter wheel mechanism.  There are square apertures in the filter holders (and the filters themselves), in the bottom and top plates of the filter wheel box, and in the filter wheel itself.  The square aperture in the top plate of the filter wheel box can be seen in Figure 9. 

 

 

 

Figure 8.  The SPIcam dewar and its filter wheel “box” are shown here.  The telescope beam enters from the top of the image.  The dewar and Cryotiger cooling head are at the bottom.

 

Figure 9.  The outer walls of the SPIcam dewar and filter wheel box have been removed to show the detector stack up inside the dewar.  The square aperture in the top plate of the filter wheel box (which is shown in red) can be seen here.  The CCD itself is barely visible in grey above the copper cold block plug seen at the bottom of the detector stack.  The cold strap between the Cryotiger cold head and the detector stack is not shown here.

 

Figure 10.  More of the support structure has been removed here to show the locations of the optically critical pieces in SPIcam.  The CCD package is seen in grey at the bottom of the image.  The blue rectangle just above the CCD is the circular dewar window, which is hidden in the figures above by the dewar lid.  The bottom of the filter box is shown in turquoise.  The filter wheel itself is shown in yellow, and just above it in light blue is shown the position of a filter in the optical path.  The filters are surrounded by a filter holder, which is bolted to the filter wheel.  The holder has been removed in this figure. 

 

Figure 10 shows best the relative distances between the CCD surface and each of the main apertures in the camera structure.  The actual distances between the silicon surface of the CCD and the bottom of each critical surface is given in Table 2.  All dimensions are in inches.  The middle column shows the thickness of each aperture.  In the case of the dewar lid, the dewar window is embedded in the lid and this thickness refers only to the metal between the CCD and the dewar window itself.  The portion of the dewar lid above the window is sufficiently far out of the beam to ignore.  In the last column of Table 2 the notations SQ. and CR. denote square and circular apertures, respectively.  Note in Figure 10 that the filters do not sit directly on the filter wheel, but are separated from it by plastic filter holders.  These holders are not shown in Figure 10.  The top of one of these holders can barely be seen in golden brown just above the yellow filter wheel in Figure 9.  The filter holders are what actually define the aperture size of the filters, rather than the filters themselves.  The holders themselves are not shown in Table 2, but their effect is to decrease the aperture size of the filters to 2.95” SQ.  Also note that the distances shown in Table 2 have been well verified.  By placing a pinhole aperture in one of the filter positions we are able to image many of the telescope apertures with SPIcam.  By knowing the true size of the tertiary cap entrance aperture, the approximate distance from the tertiary cap to the pinhole, and the size of the tertiary cap entrance aperture in a SPIcam pinhole image we can deduce the distance from the pinhole to the CCD.  Doing so yields an estimate of the filter-to-CCD distance of 3.050”.   Since the pinhole aperture does not sit exactly at the bottom of the filter holder, this distance measurement is in excellent agreement with the filter-to-CCD distance of 2.993” shown in Table 2.  Note that the active area on the CCD itself forms a detective surface that is 1.935” SQ. while the die size of the CCD is slightly larger.

 

Table 2.  Locations of Critical Apertures in SPIcam

	Distance from CCD	Aperture Thickness	Aperture Dimension & Shape
CCD Reference Plate	0.065	0.125	2.283 SQ.
Dewar Lid	0.753	0.250	3.500 CR.
Dewar Window	1.003	0.500	3.995 CR.
Filter Box Bottom Plate	2.141	0.515	2.600 SQ.
Shutter Cover Plate	2.433	.210	2.600 SQ.
Filter Wheel	2.643	.25	3.15 SQ.
Filters	2.993	.325	3.15 SQ.
Filter Box Top Plate	5.748	.515	3.20 SQ.

 

Ray tracing shows that the linear morphology of the shadowing which is seen in the flat fields can indeed be attributed to scattering within the camera. Figure 11 shows sample rays from a non-sequential ray trace through a series of apertures with dimensions given in Table 2.  The internal sides of each square aperture in this ray trace model have been made to be mirror surfaces.  An example of a ray bouncing off of one of the internal square aperture surfaces of the filter box bottom plate can be seen in Figure 11.  No attempt has been made to appropriately model the scatter of aluminum surfaces at high angles of incidence here.  I only wish to show that the scattered light profiles seen in the data are qualitatively consistent with scatter generated by the square apertures within the camera itself, rather than within the telescope.  I will present below more complete simulations that include the full beam from the telescope, but it is useful to start with the simpler system shown in Figure 11 because it illustrates well which effects are caused by scattering within the camera as opposed to scattering within the telescope. 

 

The scattered light source shown in Figure 11 has x- and y-tilts of 2.5 and 2.5 degrees, respectively.  The optical ray trace convention here is to have the z-axis be the optical axis (horizontal and left to right in the figure), the y-axis to be the vertical axis in the plane of the figure, and the x-axis to point out of the figure toward the reader.  The light source in the all the model runs shown here has a distribution characterized by the function , where the exponent N determines the angular width of the distribution.  For the simulations of Figures 11 and 12 I chose N=10, which means that the light falls off to ½ peak intensity at 21 degrees from the normal of the source plane.  I will refer to such characterizations of the source beams as “½ angles” because they denote ½ intensity points and are ½ the full angular distributions from the source normal.

 

 This choice of source distributions was somewhat arbitrary, representing a surface with more forward scattering than one would find for a Lambertian scatterer.  This choice was initially motivated by simulations which showed that light from the converging telescope beam interacting with the various apertures in the telescope is incapable of producing any significant non-uniformities in the flat fields. The f/10 telescope beam has a ½ angle of convergence of 2.87 degrees.  I have run ray trace simulations that prove that either converging or diverging beams with ½ angles less than about 3.5 degrees are incapable of producing significant non-uniformities in the SPIcam flat fields.  Later, I will show more complete telescope simulations which use what I believe are more realistic scattering distributions than that used for Figures 11 and 12, based on the flat field images and guesses of the relative brightness levels between light in the main telescope beam and light from scattering off of telescope surfaces.  But I include these early simulation examples to illustrate that there are a wide range of possible solutions if we are constrained only by the flat field images themselves.

 

 

Figure 11.  A non-sequential ray trace through the SPIcam apertures is shown in this figure.  The structures are labeled in the figure.  In this model all of the aperture plate surfaces and the CCD are absorbing except for the inner square aperture surfaces, which are assumed to be mirrored surfaces.  The filter and dewar window are BK7 glass.  In this figure only 3 of the 50 rays drawn actually made it to the CCD.  The one ray shown traveling past the CCD followed a path outside all of the plate dimensions in the model.  The line shown between the front and back surfaces in the dewar window is only the axis of a circular aperture.  A similar central line shows the axis of the circular CCD Reference Plate.  The other lines shown between surfaces of the reference plate and between surfaces of the filter box plates show the locations of their internal square apertures. 

 

 

Figure 12 shows the results of tracing 2x10⁷ rays through the system shown in Figure 11.  The figure shows the brightness distribution seen at the CCD.  The entire surface of the CCD is shown, but displayed at a 50x50 resolution to facilitate the computations.  Without the scattering from the aperture walls, the brightness distribution is uniform.  For this figure the source was set to have x- and y-tilts of 0 degrees.  The image display is inverted with dark pixels representing the brightest image regions.  The brightest peaks in this image are  9.4% higher than the dimmest.  The peaks seen in Figure 12 are approximately 1/3 of the field of view in from each edge.  This is about the location where we see the breaks appearing in the flat fields, but it is clear that this simulation does not resemble the type of shadowing which we see in the flat field data.  That will change when we consider the effects of tilts to the light source direction below.  If the source direction is not tilted, the location of the peaks is primarily dependent upon the size and distance of the aperture walls from the CCD and only weakly on the angular distribution of the light source. 

 

Figure 12.  The results of a ray tracing run through the model SPIcam apertures is shown here.  A total of  10⁷ rays were traced through the system.  A total of  4314230 of these rays hit the CCD surface either directly or after reflection from one of the interior walls of the system apertures.  The image scaling is inverted with the darkest portions being 9.4% brighter than the lightest pixels. The entire CCD surface is displayed here, but shown with only 50x50 resolution elements to facilitate the calculations. The upper left peak is seen 1/3 of the way across the image. 

 

Figure 13 shows the results of a ray-tracing run where the source direction has been tilted by 2.5 and 2.5 degrees (x- and y-tilts, respectively).  The format of this image is identical with that shown in Figure 12.  As in Figure 12 an inverted grey scale has been used in Figure 13.  Lower intensities are seen towards the upper left of the figure and higher intensities are seen towards the lower right.  Noise from the finite number of rays traced is evident in the simulation, but even with that one can see that the shadowing can be characterized by two regions resembling crossed bars which meet towards the upper left corner of the image.  The obvious explanation for this morphology is that it is generated from changes in the scattering near one corner of one of the square apertures in the system.  The morphology of this shadowing is very similar to that seen in the actual data shown in Figure 7.  The magnitude of the effect is also similar.  At the upper left corner in Figure 13 the model intensities are 21% below those seen near the lower right in the simulation.  Simulations at 5.0 and 5.0 degrees (x- and y-tilts, respectively) source tilts are not significantly different from those seen here.

 

Figure 13.  This is the result of a ray trace simulation through the aperture plates shown in Figure 11 with the light source tilted by 2.5 and 2.5 degrees, x- and y-tilts, respectively.  Like the previous simulation an inverted grey scale is used here.  The maximum shadowing seen at the top and left of this image is 21% below the peak intensities in the image that are seen at the lower right.  This simulation shows a strong resemblance to the shadowing seen in Figure 7.

 

I have shown above that the morphology of the shadowing seen in the data can be explained by scattering within the SPIcam camera itself.  But, the flat field data is the result of some combination of the type of scattering seen in Figures 12 and 13 and the light coming from the telescope beam. The light from the telescope beam is what one would normally consider as coming from the “sky”. Earlier I mentioned simulations of the telescope beam by itself (i.e. without the scattered light source shown in Figure 11) that produced perfectly uniform distributions of light on the CCD.  These simulations confirm that the contribution of the telescope beam to the flat field is simply a uniform light level which is added to distributions like that seen in Figure 13 from discreet scattered light sources.  When comparing the simulation shown in Figure 13 with all of the flat field data analyzed so far, it is clear that normally only one or two scattering sources are contributing significantly to the flat field distributions.  But, the relative contributions between the light from the telescope beam and the light from the scattered light sources are unknown without constructing careful and elaborate models of the telescope.

 

From the perspective of the scattered light source rectangle shown in Figure 11, the NA2 tunnel subtends angles between 9.5 and 25.6 degrees.  The top of the M3 cap is at an angle of 7.5 degrees and the sides of the M3 cap are at 8.4 degrees.  The aperture of the M3 cap defines the portion of the M3 mirror visible from the detector, and therefore the M3 mirror subtends angles between 0 and 5.6 degrees.  We therefore have 3 distinct angular regions from which the scattered light could be coming, corresponding to the NA2 tunnel (source angles > 10 degrees), the M3 cap (source angles between 6 and 8 degrees), and from scattering off of the M3 mirror itself (source angles < 6 degrees).  The most likely source of the scattered light is the M3 cap given the geometry of the telescope shown in Table 2.  The telescope was aligned with the moon in the middle of the enclosure slit and then offset in altitude for most of the observations analyzed here.  In most of the observations the moon was offset to higher altitudes than that of the moon.  In these cases, as the offsets get larger the low side of the M3 cap becomes more illuminated and the relative contribution of light from the telescope beam decreases.  Unfortunately, from these data alone we cannot define a unique solution without construction of a much more elaborate telescope model. 

 

However, this simple model does suggest that it is likely that the scattered light source comes from the M3 cap.  At source tilts between 5 and 10 degrees it is easiest to fit the flat field data because the contrast of the shadowing is large and this is the angular region where it is easiest to get large changes in the length of the shadow.  The increased contrast in the shadowing means that the contribution of the scattered light source required to fit the flat field data is reduced relative to that from the sky (i.e. from the telescope beam).  At small angles (< 5 degrees) the contrast in the shadowing is small (< 30%) and it becomes very difficult to produce models which fit the data without assuming that nearly 100% of the light comes from the scattered light source and almost no light comes from the normal telescope beam.  In addition to this, from the simple model shown here it is evident that the scattered light must come from angles less than 10 degrees.  Beyond this point the scattered light profile becomes more complicated than what we see in the flat field data.  Figure 14 shows one example of this.  This case is typical of what one sees in the scattered light profiles with source tilts greater than 10 degrees. The linear nature of the distribution, which we will show in subsequent simulations, is lost.  Note how the profile continues to rise at the far right of the figure.  Figure 14 was taken with N=246 (which corresponds to a ½ angle of 4.3 degrees) and with x- and y-tilts of 11 degrees, but the shape of the profile becomes more complex with smaller values of N, corresponding to broader scattered light distributions.  With broader sources the bulge in the profile seen in Figure 14 becomes more pronounced.  It also becomes more pronounced with larger source tilt angles and the location of the bulge seen in Figure 14 is insensitive to tilt angles beyond 10 degrees.  These characteristics are incompatible with the flat field profiles shown in Figures 1 through 6.   In summary, these simulations are sufficient to rule out scattering from the NA2 tunnel and suggest that small angle scattering off of the M3 mirror (< 5 degrees) is unlikely.

 

 

Figure 14.  A row through a model simulation with N=246 and x- and y-tilts of 11 degrees is shown here.  Below 10 degrees these profiles are much more linear.  The bulge seen near +5 mm in this simulation is a persistent feature of models with large source tilts (>10 degrees) and is incompatible with most of the flat field data shown in Figures 1 through 6.

 

I now show results of a simulation that includes both the scattered light source shown in Figure 11 and sky illumination entering through the normal telescope beam.  Figures 15 and 16 show the overall layout of the model.  The sky source seen at the left of the figure was given N=157,472 which corresponds to a ½ angle of 10 arcminutes.  This source angle was chosen as a computational convenience.  Narrow sources require fewer launch rays to populate the detector focal plane.  But, this distribution is just large enough to have no effect over SPIcam’s narrow field of view.  The NA2 tunnel is simulated in the model by a cylindrical, mirrored surface at the appropriate location.  Choosing a mirrored surface for this feature is clearly unrealistic, but was chosen to represent an upper limit to its effects in the simulations.  With the narrow sky source shown in Figure 15, this surface is irrelevant because no sky photons ever intersect it.  However, this feature was included in the model for studies of the effects of the NA2 tunnel when more realistic broader sky sources were chosen.  It was found to have no significant impact on the simulations, which is consistent with my earlier conclusions that the NA2 tunnel is not a significant contributor to the scattered light seen in the flat field data.  The locations of the M1, M2, and M3 mirrors are obvious in the figure.  Figure 16 shows a magnified view of the top right of Figure 15.

 

Figure 15.  This shows the optical layout of the model simulations that include sky illumination from the main telescope beam.  The blue lines coming from the source on the left simulate sky photons.  The rectangle above M1 is a cylindrical pipe that simulates the NA2 tunnel through the telescope fork.  The green lines at the top of the image show rays from the assumed scattered light source.  The structures seen within the green rays are the SPIcam apertures shown in Figure 15.

 

Figure 16.  This is a magnified view of the SPIcam structure and scattered light source seen at the top right of Figure 15.  This structure is identical to that shown earlier in Figure 11.

 

Figures 17 and 18 show the results of a simulation that closely matches the flat field data shown in Figures 5 through 7.  In this simulation the layouts of Figures 15 and 16 are assumed with the presence of both sky and scattering sources.  The scattered light source for this simulation was given x- and y-tilts of 7 degrees and N=246 (a ½ angle of 4.3 degrees).  The sky ½ angle was set at 10 arcminutes for the reasons stated earlier.  The scattered light source tilts used here are consistent with the scattering coming from the M3 cap. In this simulation the scattered light source was given an integrated intensity that was 12% of that of the integrated sky intensity.  Figure 18 is a plot of the middle row of the data in Figure 17. If the source direction of the scattered light is fixed, then the location of the break between the shadowed and non-shadowed regions of the detector is primarily determined by the chosen ½ angle of the scattered light.  The value of N in this simulation was therefore adjusted to match the location of this break seen in the flat field.  This solution is not unique.  Other combinations of source tilts, scattering angles, and relative power between sky and scattering sources can be made with equally good results.  But, as mentioned before, these choices are limited to tilt angles of less than 10 degrees and if one wishes to find a solution with tilt angles less than 5 degrees one must assume very high ratios (>1) of scattered light to sky light power.

 

Figure 17.  A simulation utilizing both sky and scattering sources is seen here.  Like earlier figures, the light distribution on the CCD surface is shown here with an inverted grey scale.  The scale to the right of the simulated image is useful only for understanding relative intensities in the image and is otherwise not in physically meaningful units.  The similarity between this simulation and the data of Figure 7 is evident.

 

 

Figure 18.  Row 25 of Figure 17 is shown in this plot.  This simulation was adjusted to match the depth of the shadowing seen at the left of the plot and the location where the shadowing stops to the data of Figure 7. 

 

 

Summary

 

The work above shows with good confidence that the scattered light that we are currently seeing in the flat field images comes from the M3 cap.  In addition, it shows with even greater confidence that the basic morphology of the scattered light at SPIcam’s focal plane is being shaped by the square apertures in the camera itself, rather than by anything in the telescope.  Light scattered off of the M3 cap enters the filter box and scatters a second time into the CCD’s field of view.  In particular, the top plate of the filter box (as defined in Table 2) is the most likely location of the aperture surface for this second scatter.  Flocking the interior walls of this aperture would help alleviate the current scattered light problems.  Both increasing the size of the filter box apertures along with flocking would be an even better solution.

 

The conclusions of this study are encouraging from the perspective of the current plans for the NA2 baffle.  As was pointed out earlier, the main function of the NA2 baffle will be to eliminate the views of the M3 cap and of the wall of the Nasmyth tunnel.  The conclusion that most of the scattered light that we see in the test flat field data comes from the M3 cap argues that most of our residual scattered light problems will be solved by the addition of the NA2 baffle as its currently envisioned.  As such, this study finds no significant reasons to alter the current conceptual design for the NA2 baffling.