Damien Jones presented PNS_09 in January 1998. This has a large field lens suitable for the VLT and it could also be used at the WHT. It served as the basis for later versions which were better optimised for WHT/TNG. Defining specifications are on the web. The VLT option has been separately reoptimised and the following new input was given to Jones for the WHT/TNG design:

optics1.ps - numerical investigation by N.G.D. to determine choice of optimum grating

optics2.ps - small changes in specifications for the reoptimisation at WHT/TNG.

Following some intermediate efforts the main versions to emerge were:

PNS_14 : compromise collimator + camera (at TNG or WHT)

PNS_15T : TNG adaptor + fixed group + camera (at TNG)
PNS_15W : WHT adaptor + fixed group + camera (at WHT)

Damien wrote "The TNG systems suffer from field curvature effects because of the smaller scale of the telescope (which makes the telescope image surface more curved) and the larger sky field (which pushes image points further out, relatively, onto this curve)."

The dedicated versions gave much better performance than the compromise one, but would have required extra optics, extra handling, and more expense. After much discussion it was decided that the WHT/TNG compromise design was probably good enough. In particular, Nigel Douglas made a simulation of the effect of seeing on the PSF and corresponding fitting error (results.V14.txt).

In the meantime Damien had optimised the camera in the compromise version and sent us this sketch:

pns3.gif

In Damien Jones' sequence of designs this is version 16 (V_16). From this file John Hart prepared the following sketch of the optical path for the two-camera design, which ND labelled with the names of the optical elements as in Tabel PNS3.18T:

duo.rays.labelled.gif

We'll refer to this as the symmetric version (V_16S) in which two gratings are used and the pupil is split.

Gabe Bloxham sent the following comments on V_16 (fax May 13) after analysing the ZEMAX files provided by Damien.

General properties :
Camera EFL 287 mm
Collimator EFL 1290.5 mm
Scale at TNG 2.78 pxl/arcsec (spec is 2.69)
Scale at WHT 3.29 pxl/arcsec (spec is 3.23)
Dispersion 2.30 pxl/A

He also traced the system using the full telescope aperture as the stop and focusing up for best image in the centre. Here is a typical example (the boxes are 49.3 microns) :

Here is a table showing rms radius (in microns) of the spots for various situations:

						
                        worst   centre	
	WHT	495nm	16.0	6.7	
                501nm	13.7	5.6	
		507nm	15.8	4.8	
	TNG	495nm	16.8	7.9	
		501nm	15.1	6.7	
		507nm	15.0	5.7	

Gabe also computed values for V_14, at our request, as this version seemed to give better performance at the TNG (but see below).

Gabe also computed the rms spot size with a "crude" simulation of the seeing (high ray density):

						
          	seeing  	centre		corner

	WHT	zero		3.5		12.2
		0.60		16.1		20.0

	TNG	zero		3.9		10.1
		0.60		13.7		16.7

Finally, Gabe computed some spots with the pupil split between TWO CAMERAS (here at somewhat higher ray density but same box size) :

For the images numbered 1-3 along the top and 4-6 along the bottom here are the r.m.s. radius values in microns compared with for the one-camera case:

		one-camera	14.2 14.2 16.0 6.8 12.7 13.5
		two-camera	 9.0 15.7 12.4 4.0 12.6  6.4

                CENTROIDING ACCURACY WITH THE PNS


In the presence of uniform noise (i.e., background-limited work), the
PSF-fitting centroiding accuracy from these can be estimated with the
formula 

                              (rms noise per pixel) 
(delta_x) =  ----------------------------------------------------------------
           sqrt[ integral (dPSF/dx)^2 dx dy ] * (counts in image) * pixel size

where the PSF is normalized to unit integral. For a gaussian image,
of x- and y-dispersions sx and sy, this yields

              sqrt(8 pi sx sy) * (noise per pixel) 
(delta_x,y) = ------------------------------------- (sx, sy)
                    counts * pixel size

I have calculated the same quantity for the PSF's derived by
gauss-smoothing the spot diagrams. The table below shows the
results. The last line (`perfect spot') shows the centroiding accuracy
due to the seeing alone.


There are also plots showing the spots themselves, and the images
smoothed by gaussians with FWHM 0.3, 0.5, 0.8, 1.0", for the different
models, one model to a page. Each model is shown on WHT and TNG., at
field center (position 1) and in a corner (position 6). Smoothed spots
are contoured at levels a factor 10**(0.5, 1, 1.5, 2) below the peak.


Table. 1-sigma centroiding error for the various models, in arcsec,
for a source of unit flux, in background noise with rms noise of 1 per
square arcsec. The error scales linearly with the rms noise level, and
inversely with the brightness of the source. For each model, 1st line
is x-error, 2nd line y-error.

    MODEL       seeing=0.3     seeing=0.5     seeing=0.8     seeing=1.2
               Pos 1  Pos 6   Pos 1  Pos 6   Pos 1  Pos 6   Pos 1  Pos 6
a_tng_l_*-501  0.090  0.205   0.224  0.351   0.546  0.678   0.842  0.977
               0.084  0.172   0.196  0.299   0.462  0.572   0.706  0.820
a_wht_l_*-501  0.083  0.145   0.215  0.278   0.536  0.599   0.833  0.896
               0.073  0.123   0.184  0.237   0.448  0.507   0.692  0.753

b_tng_l_*-501  0.089  0.141   0.223  0.284   0.545  0.611   0.841  0.909
               0.078  0.145   0.192  0.279   0.460  0.556   0.705  0.803
b_wht_l_*-501  0.082  0.129   0.215  0.265   0.536  0.587   0.832  0.883
               0.072  0.102   0.183  0.212   0.448  0.476   0.692  0.719

c_tng_l_*-501  0.097  0.270   0.232  0.424   0.555  0.745   0.852  1.039
               0.091  0.228   0.206  0.360   0.475  0.624   0.720  0.865
c_wht_l_*-501  0.088  0.170   0.221  0.302   0.542  0.624   0.838  0.921
               0.080  0.154   0.191  0.266   0.457  0.535   0.701  0.782

d_tng_l_*-501  0.094  0.193   0.230  0.328   0.554  0.647   0.851  0.943
               0.083  0.152   0.200  0.274   0.473  0.544   0.719  0.789
d_wht_l_*-501  0.086  0.160   0.220  0.299   0.542  0.619   0.838  0.915
               0.076  0.120   0.189  0.229   0.456  0.493   0.700  0.736

PERFECT SPOT   0.074  0.074   0.205  0.205   0.524  0.524   0.819  0.819
               0.060  0.060   0.168  0.168   0.429  0.429   0.671  0.671

Model a=V16 model, full pupil
Model b=V16 model, half pupil
Model c=V14 model, full pupil
Model d=V14 model, half pupil

Conclusions:

- Seeing effects are pretty much dominant for all models above seeing
  of 0.8". On axis, the same is true down to 0.5", but the off-axis
  position 6 gives centroiding errors as much as a factor 1.6 larger
  than on-axis. Using only half the pupil largely cures this problem.
- There is little difference between V14 and V16, at least
  as far as the spots analysed here are concerned, with V16 winning in
  each case.  
- The spectrograph performs slightly better on WHT compared to TNG, 
  but the difference is small.

STRAY LIGHT PROBLEM

On May 14, 1999 John Hart informed us of a problem discovered by Gabe Bloxham during ray tracing of the spectrograph with the concave mount (and as flagged earlier on the checklist page).

It turns out that there is a problem at the very simple zero order level. Treating both gratings as mirrors, some of the light which reflects off the first grating strikes the second grating at near grazing incidence, and then reflects into the camera over much the same angular range as light which arrives by the intended path. Thus, the stray light produces a spatial image which is almost coincident with the spectral image. Because there are two reflections involved, the spatial image will be inverted wrt the spectral image.

We have no quantitative estimate of intensity, but I imagine this is a serious problem. The first reflection should be well attenuated because most of the energy goes into the blazed order (note added by ND: expect about 10% into zero order), but the second reflection will be fairly efficient because it is at near grazing incidence.

In effect, the spatial image beam goes into the unused half of the camera, and so some of it can be baffled. But rays coming from near the grating split are overlapped with the true beam, and so can't be baffled.

On May 18 Damien Jones confirmed this (in his notation 0,2 means m=0 at the first grating then m=2 from the second grating):

The 0,0 ghost is imaged onto the detector, offset by about 7 mm. The 0,2 ghost at the centre wavelength is imaged in the plane of the opposite camera's detector with a large offset. The absence of a direct image doesn't necessarily imply an absence of stray light from a bright source, or a direct image at a close wavelength let through by the filter.

The convex arrangement is much more benign:
the 0,2 ghost passes back into the collimator. A portion of it may be back reflected by the blocking filter if its back surface is not AR coated as well.

Steps to take:

1. Modify the double grating mount from a concave arrangement to convex.
2. AR coat the rear surface of the blocking filter.

Gabe also spotted another potential ghost problem. There is an out-of-focus ghost formed by a first reflection off the detector and a second off the leading surface of the SK16 positive element in front of the field flattener. It falls off very rapidly away from the optical axis. This ghost should not be a problem if the AR coatings are properly designed but we need to be aware of it (a note has been put on the checklist - ND).

There has been some discussion about "crossed gratings". To make this unambiguous here is a figure in which crossed gratings are shown in the UPPER part of the drawing. the LOWER part is our "convex" grating arrangement.

It seems to N.D. that the crossed gratings will make the exiting beams too large for the camera optics. Right now the 190mm beam is sliced in two and then anamorphically magnified by cos(35) to give a final diameter of around 116mm. Since 116 < 190 it is the size of the beam in the NON-DISPERSED direction which determines the requires size of the optics. With crossed gratings the output beam is 2x larger i.e. 232mm, two large for the current optics.

Gabe (25 May 1999) raised other objections:

Point #1. When the dichroic beamsplitter is inserted or removed, the pupil image will jump across this split line by a total movement of approx 6.3mm, in the "x-axis", because the grating axis is displaced by 3.15 mm as per design to minimise the size of the grating. This results in a change of intensity of the axial beam of approx 3.0+ %. (I agree: but such a small departure from 50:50 splitting is OK)

Point #2. This crossed grating plan, will result in progressively worse shadowing, and hence loss of light, from "off-axis" field positions, as the exposed edges block light reaching (and leaving in the other half) the other grating. A quick calculation show this to be approx 3% from center to worst corner of the field. In fact the loss will be worse than this, because these edges must have bevels as well, as per the instruction from the Richardson Grating Lab of minimum dimension of 1.5 mm face width, for replication reasons.

(So crossed gratings look like a poor answer to this problem).