This document describes various options for the configuration of the Integral Field Unit (IFU) in the Gemini Near-infrared Integral Field Spectrograph (NIFS), and the effects they have on the performance and manufacturability of the IFU. The document concludes with the selection of a particular configuration.

2 Applicable Documents

Document ID	Source	Title
	RSAA	NIFS Conceptual Design Review Documentation Vol. 1

3 Introduction

The concentric IFU concept described in the Gemini Near-infrared Integral Field Spectrograph (NIFS) CoDR document has been adopted, but it needs further development to overcome some practical difficulties.

In the ideal concentric system, the channels of the IFU are fanned about a common axis that passes through the center of the image slicer in a way that makes the channels optically identical, except that they are fed from different levels within the image slicer stack. If the single-channel optics are designed to give good imagery over the whole un-sliced field, then each channel will perform well with its particular slice.

If the fanning axis is regarded as the azimuth axis of the system, then the geometrical principles required to achieve this ideal can be explained as follows.

· The curved surface of the image slicer should be tangential to the fanning axis at its center. This is the condition for which all channels have the same set altitude angles, and the mirror arrays are circularly symmetric. An additional desirable feature is that the azimuth angle of each slice is exactly half the azimuth angle of the corresponding channel.

· The aluminium alloy plates onto which the pupil and field mirror elements are machined should be perpendicular to the fanning axis. This allows all the mirror elements of the circularly symmetric arrays to be mechanically centered in the plates.

· The off-axis angles for all three mirror elements in the channel (slicer, pupil mirror and field mirror) should be made no larger than is needed to avoid beam interference with adjacent components. This minimizes the astigmatism produced by the element. Suitable off-axis angles are, for the slicer, 1°, and for the pupil and field mirrors, 5°. The slicer and field mirrors only produce aberration in the pupil images, and so this requirement is less stringent for these than for the pupil mirror.

Applying these principles with varying degrees of rigor, a number of optional configurations are examined in the following section. In the diagrams shown for each option, the IFU fanning axis is a vertical line passing through the center of the image slicer and the center of the diffraction grating. It is, in effect, the azimuth axis of the IFU.

4 Optional Configurations

4.1 Configuration A

Figure 1: Configuration A

This is the baseline configuration presented in the CoDR documents (volume 1, §4), and is shown here in Figure 1. It complies with all the principles listed above, and is in this respect the optimal system. Nevertheless, it has certain practical problems.

A characteristic of the configuration is that the pupil and field mirror elements are tilted with respect to plates on which they are machined. This means that the relatively fast beam emerging from the field mirror has a very shallow angle with respect to the pupil mirror array plate, and for the beams coming from the lower elements of the slicer, there is a clearance problem. This would require that the back end of the pupil mirror array plate be relieved.

More importantly, however, there are repercussions for the diamond machining of the arrays. As explained in the CoDR documents (volume 1, §4.21.1.2), it is proposed that a flycutting technique be used to generate both the torroidal elements on the pupil mirror array, and the spherical elements on the field mirror array. The surfaces that this produces are not true torroids or spheres, but a good approximation is made if the vertex of the actual figure is at or near the center of the element. To achieve this, the array plates must be tilted in the diamond machining mill so that the normal to the element surface at the element center is perpendicular to the spindle axis of the flycutter.

In principle, this correction leaves aberrations in all but the central element of each array, because the required tilt differs slightly for each element. This effect is small, however.

A further complication is that, because the array plates are tilted, the toolpath has to be adjusted in height for each element of the array.

None of these difficulties is intolerable, but their avoidance is very desirable. Given that the production of the IFU is seen as one of the most demanding aspect of the NIFS project, it is important that it be simplified as much as possible.

4.2 Configuration B

Figure 2: Configuration B

This configuration is shown Figure 2. It complies with the principles listed in the introduction, except that the off-axis angles at the slicer are increased to match those at the pupil and field mirrors (5°). This has the effect of squaring the pupil and field mirror elements to their respective array plates, and so eliminates all the array problems described for configuration A.

The cost of this improvement is that aberrations are considerably increased in the pupil images. This effect is shown in Figure 3, using configuration A as the benchmark.

Figure 3: Pupil Image Aberration. Boxes are 0.5 mm square.

The curve shown in each box is an image of a point on the center of the cold stop, as formed on the pupil array element by the single slice of the slicer corresponding to the specified channel. The slice is then the pupil of this subsystem. The aberration “spot diagram” appears as a line because the slice is thin. The boxes are centered on the array mirror element. Ideally, the image should be a point in the center of the box.

Pupil image aberration is mostly caused by the off-axis angle of the image slicer. The only configuration considered which has an enlarged off-axis angle is B, and it is therefore the only one with degraded optical performance. Pupil aberration for configurations C and D are not shown because they are similar to those for configuration A.

The slices are made by machining them to a common spherical surface before fanning, and so the aberration produced by the off-axis angle is largely astigmatism. Because there is only a small margin between adjacent pupils on the array, the common curvature of the slices is chosen to minimize image spread in that direction, and allow astigmatic spread in the perpendicular direction. Because each pupil image is formed by a single slice, more-or-less off-axis, the aberration manifests as a displacement as well as a smearing.

Displacement along the array, but not perpendicular to it, can be corrected by adjusting the fanning angle of the slice. This correction has been made for configuration B, but not for the better performing configuration A.

The boxes shown in Figure 3 are 0.5 mm square. The geometrical diameter of the pupil image (for a telescope aperture of 8 m) is 1.75 mm. To account for diffraction at the slicer, the optical system is designed to capture a pupil elongated by 0.53 mm in each direction perpendicular to the array (up and down in Figure 3). For the near channel of configuration B, the maximum vertical displacement caused by aberration is 0.24 mm. This is excessive relative to the pupil dimensions specified.

Image spread in each direction along the array is a maximum of ±0.02 mm. This is acceptable compared to the margin of 0.17 mm.

Aberrations in the field images are not discussed here because they are much the same (and acceptable) for all the configurations considered.

4.3 Configuration C

Figure 4: Configuration C

This configuration is shown in Figure 4. It complies with the principles listed in the introduction, except that the center of the slicer is not tangential to the fanning axis. Rather, the curved slicer face (but not the mechanical stack) is tilted downwards by 4°. Simultaneously, the pupil and field mirror elements can then be square to the array plates, and the off-axis angle of the slicer can be its desirable 1°. This avoids both the array manufacturing problems of configuration A, and the pupil aberration problems of configuration B.

The penalty of this arrangement is that the fanning geometry is no longer ideal. When the center of the slicer is not tangential to the fanning (azimuth) axis of the system, the altitude angle of the reflected ray varies as the azimuth angle of the slice changes from channel to channel, and the azimuth angle of the reflected ray is no longer simply twice the azimuth angle of the slice.

The azimuth deviation is easily corrected by adjusting the angular spacing of the slices, but the varying altitude angle causes the pupil images to be located at different heights on the pupil mirror array. The azimuth angle correction, and the altitude angle error are determined with reference to Figure 5.

Figure 5: Alt-Az Reflection Geometry

In this, the reflecting surface of the slicer is at point 0. Points 0,1,2 and 3 lie in the reference plane perpendicular to the azimuth axis of the IFU. Points 0, 4, 5 and 6 lie in the ray plane. Line 0-5 is the normal to the reflecting surface.

Any three of the angular parameters shown fully define the geometry, and the remaining three values can be determined from the following three equations. For NIFS, A, B and D are the pre-defined parameters, so the equations can be applied directly.

If D is small (as it is for the IFU), these equations can be simplified as follows.

The deviation in altitude angle of the channel at angle D from that of the central channel can then be expressed as

If additionally A and B are small (as they are for NIFS), the equations can be further simplified as follows.

The two levels of simplification shown above are both relevant. In the second level, the equations for F and ΔC are useful, but that for E is not because it has degenerated too far. For this, the first level version must be used.

For the proposed layout, the altitude angles of the incident ray and the slicer surface normal are respectively

and

Applying the foregoing equations, the corrected ratio of slice azimuth angle to channel azimuth angle is

The length of the slit images on the field mirror array must match the circumferential pitch of the mirror elements. From the CoDR document (volume 1, §12.2), the angular length of each slice, referred to the sky, is 14.5301 mrad. Given that the focal length of the telescope is 128 m, the distance from the image slicer to the field mirror array is 420 mm, and that there are 29 channels, then the azimuth angle of the outer channels is

The azimuth angle of the corresponding slices is then

And the deviation in altitude angle of the corresponding reflected rays is

Given that the distance between the image slicer and the pupil mirror array is 448 mm, the maximum deviation in the position of the pupil images on the array is 30 mm. In relation to the pupil image data given in §4.2, this error is negligible. In fact, the maximum pupil deviation could be halved by sharing it equally between the central and outer channels, but the error is so small that this additional correction is not warranted.

4.4 Configuration D

Figure 6: Configuration D

This configuration is shown in Figure 6. It is the same as configuration C, except that a different fanning method is used for the image slicer. The fanning axis of the slicer stack is tilted so that it is tangential to the slicer face at its center. This axis is then no longer coincident with the fanning axis of the pupil and field mirror arrays, which remain vertical. The interface planes of the slicer are perpendicular to its fanning axis.

The purpose of this variation is that it conveniently allows the pre-fanned slicer stack to be mounted concentrically in the chuck of the diamond turning lathe during manufacture. This makes balancing of the chuck easy, although it could be argued that an eccentric mount is better because is avoids the risk of producing o’jives and center pips.

A secondary reason for the variation is to investigate the effect that it has on the deviant alt-az reflection geometry described in §4.3.

Using the nomenclature defined in §4.3, it is clear from first principles that for small angles

The deviation in the height of the pupil images for this configuration is therefore twice that for configuration C, or 60 mm. While this is acceptably small, the degradation is probably not justified by the ambiguous production advantage.

5 Conclusion

Configuration C appears to be the best option, provided it can be conveniently folded into the ill-fitting cryostat. A consideration in this regard is that the focal ratio converter system has been inverted with respect to that shown for configuration A (for which folding conditions have already been established). This was done because it results it the input beam to the focal converter being aligned to the coordinate system of the optics (perpendicular to the azimuth axis). Otherwise, it would be sloped at 6°. If necessary, configuration C could be changed in this regard.

Appendix A: List of Figures

Figure 1	configuration a.wmf
Figure 2	configuration b.wmf
Figure 3	pupil aberration.wmf
Figure 4	configuration c.wmf
Figure 5	alt-az reflection geometry.wmf
Figure 6	configuration d.wmf