
Optical Design for Off-Axis Collimator Report
Bench Upgrade Project
Matthew Bershady, Project Scientist
Version 1.1, Jan 04 2006 

SUMMARY

This report contains

(1) a summary of the latest optical design work from Charles Harmer
(CH) on the off-axis collimator for the Bench upgrade (completed on or
before 11 Aug 2005) in terms of pupil distance and layout of
spectrograph elements; and

(2) a completed analysis on the optimum pupil placement and overall
spectrograph layout to achieve the following three goals: minimize
vignetting, allow for echelle configurations at 11 deg off-Littrow or
more, and avoid parasitic light from entering camera.

My conclusions are (i) the existing optical models have sufficient
range of pupil distances to be acceptable as final designs; (ii) the
optimum back-distance of the first grating/fold-flat turret from the
collimator (off-axis paraboloid segment) is 1170 mm for a pupil
distance of 1620 mm.

My specific recommendation is to adopt one of these optical models
with a pupil distance of 1620 +/- 10 mm from the collimator: 

	PlaneSC_5X_Bias_f5_4el_14deg_NP_7a_folded+316ech9.zmx
	PlaneSC_5X_Bias_f5_4el_14deg_NP_7_folded+316ech9.zmx

and construct final models with the geometry for the collimator,
grating, and camera distances specified in Tables 1, 2, and 3 below.

This recommendation assumes the image quality of the current optical
models meets our specifications. My understanding from conversations
with Charles Harmer is that this is indeed the case.  A final version
of this report will include a preliminary assessment of image quality
to provide documentation that this assumption is valid.

Separate reports will discuss (a) tolerancing and optomechanical
design issues, (b) physical layout issues; and (c) final image
quality assessment relative to the current system.

An Appendix to this report includes the specific spectrograph
configurations to be generated to conclude item (c) above.


1. Basic description of latest optical design work:

The latest design from CH includes a 4-element corrector of tilted,
all-spherical, all-glass elements. This delivers a ~160 mm collimated
beam diameter for an f/5 input. The design now appears to allow for a
range of pupil distances between at least 1373 and 1628 mm from the
collimator.  This web site is being built to illustrate and archive
the optical design work:
www.astro.wisc.edu/~mab/research/bench_upgrade/oap/design.html.

CH has explored the extreme, off-blaze echelle configuration in order
9 centered near 660 nm (Ha rest). The grating angle is 76.5 deg, which
leads to significant vignetting at the grating, even with the shorter
collimator.

The final image-quality assessment and pupil placement optimization
needs to consider a larger range of spectrograph configurations.
However, CH has used this grating configuration to effectively
illustrate several key issues regarding vignetting for the
implementation of the echelle -- the most demanding. These involve the
following issues.

a. the camera-collimator angle: 

	o explored 11 to 13 deg;
	o current system uses 11 deg.

     	Lower angles give higher diffraction efficiency but more
	vignetting from camera obstruction or larger distances between
	optical elements.

b. the grating-camera distance: 

	o explored 500 to 1016 mm;
	o current system uses 390 mm (low-order grating) to 1016 mm
	  (extreme echelle).

	Larger distances increase spectral vignetting, but can reduce
	vignetting from camera-obstruction of the grating-incident beam.

c. the collimator-grating distance: 

	o explored  800 to 1428 mm;
	o current system uses 1839 mm (all gratings)

	This distance is of no consequence to the vignetting as long as 
 	the pupil distance can be controlled. Long collimator-grating
	distances allow for larger grating-camera distances that avoid
	(a) physical collisions between camera and collimator for 
	small camera collimator angles used with the echelle (e.g., 11
	deg); and (b) parasitic light entering camera (see discussion
	below).

d. the collimator-pupil distance: 

	o explored 1373 to 1628 mm;
	o current system uses 1021 mm.

	this distance is critical for minimizing the vignetting. In
	general the optimum placement is between the grating and
	camera (see discussion below), and therefore the optimum
	collimator-pupil distance depends on the collimator-grating
	distance and the grating-camera distance. The longer the
	collimator-pupil distance, the larger the required collimator,
	but this is not a significant effect for range considered here.

Assuming the achieved optical image quality is largely independent of
these parameters, then they are important only for minimizing the
system vignetting in various configurations.

Conclusions from review of the optical design:

The collimator-grating distance must be large enough to allow a large
enough camera distance in the 11 deg echelle configuration to avoid
beam obstruction and physical collisions with the collimator, yet
still allow the camera to be sufficiently in front of the collimator
to avoid parasitic light from entering the camera.  (Parasitic light
here is direct injection of un-dispersed light from the fibers into
the camera objective.) This issues was not properly addressed in the
15 Sep 2003 Report, and so it is critical that it has been addressed
here.

The pupil distance (from the collimator) must be large enough to
accomodate the required collimator-grating distance. Luckily we can
take advtange over control of the pupil placement in the current suite
of models to finesse the situation.


2. Pupil placement and layout analysis

There are 3 elements to the analysis:

a. Vignetting: placement of the pupil must minimize the overall
   vignetting contributed by the grating and camera combation.

b. Obstructions and physical collisions: the pupil distance must allow
   for a camera-collimator angle of 11 deg with sufficient back-distance
   such that the camera and collimator do not collide and such that
   the camera does not obstruct the collimator beam incident on
   the grating.

c. Parasitic light: the pupil distance must allow for a camera distance 
   in FRONT of the collimator sufficient to avoid parasitic light.

a. Vignetting

In the 15 Sep 2003 Bench Ugrade report, MB presented the optimum pupil
placement for different grating and camera-collimator angles (Fig
20). This assumed a collimator-grating distance of 800 mm, and
grating-camera distances of 1016 mm for the echelle and 390 mm for the
low-order gratings. (Note that camera back-distances as low as 805 mm
are also used with the echelle in extreme off-order configurations.)
The optimum pupil placement to minimize vignetting is roughly 2/3 the
distance between grating and camera objective, despite the fact that
the camera objective is larger than grating.  (This is due to the
combined effects of dispersion and field angle.)  A reasonable
compromise for echelle and low-order configurations was to place the
pupil at a collimator distance of 1250 mm.  However, this assumed a
collimator-grating distance of 800 mm, which is too short to
accommodate the echelle configuration and avoid parasitic
light. 

*** Assuming we can always have a sufficiently large collimator to
*** accommodate the desired pupil distance, what is relevant is not the
*** pupil distance from the collimator, but the pupil distance in relation
*** to the grating and camera. In these terms, the 15 Sep 2003 report
*** prescribes the pupil be placed 450 mm beyond the grating as a
*** compromise between low-order and echelle configurations.

Other considerations:

For the upgraded spectrograph, the 1016 mm grating-camera back
distance can be decreased to 983 mm or less (see below). This has an
insignificant impact on the above calculation.

However, for the VPH gratings there are two modes: direct and folded.
In the direct mode, the grating-camera distance is slightly lower than
the low-order SR configurations (356 mm instead of 390 mm). In the
folded case, the grating-camera distance is even smaller (206 mm), but
since the grating is down-stream of the first grating turret (which in
this folded mode houses the fold-flat), the relevant distance is
really the fold-flat--camera distance. The latter is intermediate
between the SR/direct-VPH and echelle configurations (739 mm).  This
mean the 450 mm pupil back-distance from the first grating turret is
still close to the best compromise for all configurations. 

THIS 450 mm PUPIL BACK-DISTANCE FROM THE FIRST GRATING TURRET IS THE
ADOPTED FINAL VALUE.

TABLE 1. Grating-camera distance summary

echelle-existing	1016 mm
echelle-existing	 805 mm extreme off-order
echelle-upgraded	 983 mm
low-order SR		 390 mm
VPH direct		 356 mm
VPH folded		 206 mm
			 739 mm starting from fold-flat

TABLE 2. Distance from the pupil 

			flat		grating		camera
echelle-existing	NA		-450 mm		+566 mm
							+355 mm	extreme off-order
echelle-upgraded	NA		-450 mm		+533
low-order SR		NA		-450 mm		- 60 mm
VPH direct		NA		-450 mm		- 94 mm
VPH folded		-450 mm		+ 83 mm		+289 mm

   Note: + pupil is beyond element; - pupil is in front


b. Obstructions and physical collisions.

The grating back-distance from the collimator must accommodate an 11
deg camera-collimator angle and grating-camera distance to keep the
collimated f/5 beam (diameter of 160 mm) incident grating beam
unubstructed by the camera housing. An estimate can be made by
assuming a perfect f/5 beam. The camera geometry
(www.astro.wisc.edu/~mab/education/astro920/camera.jpg) implies:

	d_gc >= (80 mm + 109.5 mm cos theta_cc) / sin theta_cc

where d_gc is the grating-camera distance; 80 mm is the beam radius;
109.5 mm is the camera-housing radius taking into account the 13.4 deg
wedge taken out of the inner, front face; and theta_cc is the
camera-collimator angle.

This yields a conservative maximum grating-camera distance of 982.6 mm
(roughly 39.7 inches) for theta_cc = 11 deg. It is a conservative
(i.e., optimum distances are likely shorter) because the beam is soft,
and larger d_gc increases the spatial and spectral vignetting.

From this I conclude the grating must be at least 983 x cos (11) =
965 mm from the OAP, as measured from the beam center.


c. Parasitic light.

The camera objective must be sufficiently in front of the OAP such
that irradiance from fibers toward collimator does not enter the
camera. Fig. 18 of the 15 Sept Report indicates there is power out to
f/3.5, and power at the 1% level at f/3 would not be surprising.  Some
of this can be mitigated by baffling the beam in the toes and
(preferably) in the corrector housing. But in general, the pupil
distance must be large enough to accommodate an efficient echelle
configuration at 11 degree camera-collimator angle.

I conclude the beam should be baffled for f/4, i.e., i.e., the
baffling must be such that the beam incident on the collimator is no
faster than f/4, while the returned, collimated beam is also allowed
to be up to a diameter of 200 mm at all field positions.  The nominal
design is for f/5, but there is significant power out to f/4 (10-15%),
some of which will make it through the system for various fibers and
configurations.

I estimate that the camera objective should be about 53 mm in front of
the OAP (toward the grating). Add another 1-2 inches (25-50mm) to be
safe.

From this I conclude a collimator-grating distance of no less than 965
+ 100 = 1065 mm. This can be compared to the value of 1840 mm for the
current system.


Summary of considerations (a-c):

This implies pupil distances of roughly 1065 + 450 = 1515 mm, which is
in the range of modeled pupil distances. 

None of the models have exactly this pupil distance, so I recommend
adopting either PlaneSC_5X_Bias_f5_4el_14deg_NP_7a or
PlaneSC_5X_Bias_f5_4el_14deg_NP_7, which yield 1609 and 1628 mm pupil
back-distance respectively, as long as this pupil distance does not
cause problems for the spectrograph layout (the difference between
this and the nominal optimum collimator-pupil distance is about 100
mm). We then have the following nominal final values:

TABLE 3. Distance from the collimator

collimator-pupil distance:		    1620 mm
collimator-grating (first-turret) distance: 1170 mm

This, in combination with the above table for the distance of optical
elements from the pupil completely defines the spectrograph layout.


3. Image quality

I have not yet assessed image quality of the 8 designs with varying
pupil distances. My understanding from CH is that pupil-distance has
little effect on the optimized image quality in this series of
4-element designs.

I will make an initial internal comparison, as part of the final version 
of this report of the 8 different models.

The final analysis will be a direct comparison to previous models of
echelle and non-echelle configurations for the existing system and
the earlier off-axis designs with 3 corrector designs circa the 15 Sep
2003 Upgrade Report.


4. Some questions about the current design:

   o is the control of the pupil placement continuous in the 1300-1600
     range?

   o should the lenses be somewhat larger in the z dimension to avoid
     vignetting or scattering at the edges of the slit?



APPENDIX:

Here we define a set of model configurations for final image-quality
analysis.

The 4-element OAP designs generated to date are for the order-9 setup.
This has the highest dispersion and anamorphic factor, and therefore
is critical to compare for preserving this high-resolution mode.  (The
anamorphic factor is not relevant in the comparison itself since we
are only looking at the optical aberrations.)

However, this configuration also has very large grating angles, and
therefore significant vignetting. The order 8 Ha setup has among the
the lowest angles, and hence minimizes vignetting in both the
existing and proposed systems. Comparing this configuration therefore
also has merits. For reference, here are the maximum echelle grating
angles that do not vignette an unobstructed f/5 beam at the pupil:

	f/5 at 800 mm (short): 160 mm beam	66.8 deg
	f/5 at 1021 mm (Long): 204 mm beam	59.8 deg

With the final pupil distance and spectrograph established (this
document) we should now commence generating a set of models that match
the grating setups used for the Sep'03 report.  I would like to
request the following.


grating	order	cwl	alpha  theta_cc f-	collimator 	collimator
					ratio	effective f.l.	type
echelle	11	5130	69.1	11	5.0	800		14deg OA, 4-el
echelle	9	6619	76.5	11	5.0	800		14deg OA, 4-el
echelle	8	6687	63.5	11	5.0	800		14deg OA, 4-el
echelle	8	6687	63.5	11	5.0	1021		existing on axis
600@10	1	5700	25.2	30	5.0	800		14deg OA, 4-el
316@7	1	7450	22.0	30	5.0	800		14deg OA, 4-el

grating	order	cwl	alpha	flat	f-ratio	collimator 	collimator
				angle		effective f.l.	type
740 VPH	2	4883	21.0	22.5	5.0	800		14deg OA, 4-el
740 VPH	2	4883	21.0    22.5	5.0	1021		existing on axis

Notes - 

 * flat angle is the angle between the fold-flat normal and incident beam.
 * collimator type: "14deg OA, 4-el" refers to the current design with a pupil
   distance of 1620 +/- 10 mm.
 * all configurations for the "14deg OA, 4-el" collimator should have a
   collimator-grating or collimator--fold-flat (first-turret) distance of
   1170 mm.
 * the configurations for the "existing on axis" collimator should have a
   collimator--fold-flat (first-turret) distance of 1839 mm.
 * grating-camera distances should be as follows for the "14deg OA, 4-el"
   system:
	echelle	 	983 mm
	low-order SR	390 mm
 * fold-flat--grating distances and grating-camera distances should be
   as follows for both collimators:
	fold-flat--VPH	5333 mm
	VPH-camera	206 mm

