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AUSTRALIAN
NATIONAL UNIVERSITY System Design Note 5.06 Created: 4 April 2000 Last modified: 4 April 2000 |
NIFS DIFFRACTION ANALYSIS
Ian Price
Research School of Astronomy
and Astrophysics
Institute of Advanced
Studies
Australian National
University
Revision History
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Revision No. |
Author & Date |
Approval & Date |
Description |
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Revision 1 |
Ian Price 18 August 1999 |
Jan van Harmelen 01 October 1999 |
Original document. |
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Revision 2 |
Ian Price 22 October 1999 |
Peter J. McGregor 28 October 1999 |
Added OH line profile analysis. Modified discussion and grating length constraints. |
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Contents
1 Purpose
The purpose of this document is to discuss diffraction effects in the Gemini Near-infrared Integral-Field Spectrograph (NIFS). NIFS will use 0.1˛ wide slitlets which are comparable in width to the Gemini telescope diffraction size at 2 mm. Masking of image plane with a slit and restricting the extent of the pupil image cause diffraction effects which must be considered in the instrument design. These effects are modeled to determine optimal dimensions for the NIFS pupil mirrors and diffraction gratings.
2 Applicable Documents
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3 Introduction
The Gemini Near-infrared Integral-Field Spectrograph (NIFS) is intended to perform near-diffraction-limited imaging spectroscopy at near-infrared wavelengths. It will use 0.1˛ slitlets which are only slightly larger than the 0.07˛ full width at half maximum of the telescope diffraction pattern at 2.2 mm. Such narrow slits cause diffraction effects in the spectrograph dispersion direction that broaden the beam beyond its geometrical size. These effects must be considered in arriving at suitable dimensions for the NIFS pupil mirrors and diffraction gratings. The finite lengths of the pupil mirrors and diffraction gratings also mask the pupil images. This causes a second diffraction effect that alters the profiles of monochromatic slit images at the detector. This effect must also be considered in order to ensure that diffraction effects do not limit the degree of rejection of OH airglow emission-lines.
The method used to model diffraction effects in NIFS is described in this document. The resulting loss in system throughput and reduction in image quality are investigated as functions of the grating dimension and the off-axis angle of the source in the dispersion direction.
4 Diffraction Model
Diffraction effects in NIFS have been modeled using a Fourier technique that assumes perfect geometrical optics. Fast Fourier transformations (FFTs) are used to progress from the telescope pupil plane through the telescope image plane, the pupil mirror plane, the field mirror image plane, the grating pupil plane, and finally to the detector image plane. The image and pupil planes are both sampled on a 512´512 pixel grid. Transformations from pupil planes to image planes are performed with a forward FFT, and transformations from image planes to pupil planes are performed with an inverse FFT. The sampling resolution is 80 mm/pixel at the telescope pupil, 13.5 mm/pixel at the pupil mirror plane, and 312 mm/pixel at the grating. The image scale is 0.005l arcsec/pixel where l is the wavelength in microns. The transmitted transforms are masked as appropriate at each plane. The telescope pupil is modeled as a 7900 mm diameter circular aperture with a central obstruction 1023 mm in diameter and a four vane spider with 5 mm thick vanes. An effective telescope focal length of 712,580 mm was used to produce an f/90 image on the integral-field unit (IFU) image slicer. The image plane at the image slicer was masked with a 0.1˛ wide slit representing one slice of the IFU image slicer. A pupil image is formed 120 mm from the image slicer at the pupil mirror array. This pupil image is masked by a rectangular aperture 2.0 mm wide (in the slit direction) and 4.0 mm long (in the dispersion direction) representing a single pupil mirror. The pupil mirrors reimage each IFU image slicer slitlet onto its corresponding mirror in the field mirror array where the reformatted “staircase” slit image is formed. The field mirrors are each 2.0 mm ´ 4.0 mm and do not vignette the image. The 501 mm focal length collimator reimages the pupil on to the diffraction grating. Since the angle of incidence at the grating is approximately 35°, the physical length of the grating must be at least a factor sec 35° larger than this pupil image in the dispersion direction. The reformatted slit image is reimaged on to the detector by the 290 mm focal length camera. It is assumed throughout that the telescope optics produce a perfect diffraction-limited image at the image slicer with no distortion due to atmospheric seeing or optical aberrations. It is the purpose of the ALTAIR adaptive optics system to deliver such an image. The reflectivities of all surfaces, including the grating, are assumed to be unity.
The pupil images formed at the pupil mirrors are reimaged at the grating with the image dimensions scaling as the ratio of the collimator to field mirror focal lengths. The 2.0 mm ´ 4.0 mm pupil mirrors then map to 46.4 mm ´ 92.8 mm at the grating pupil. The sec 35° projection factor due to the grating inclination requires that the gratings be at least 113 mm long to prevent further vignetting at the grating pupil. NIFS will use a grating wheel to change between gratings. Geometrical constraints on this wheel provide a joint constrain on the length and number of gratings that can be accommodated. The dimensions of the duplicate NIRI cryostat constrain the grating wheel diameter to < 300 mm. Accommodating the basic set of four gratings limits the length of each grating to be < 125 mm, which is compatible with the pupil mirror constraint. We investigate diffraction effects for grating sizes ranging up to 113 mm.
5 Diffraction Analysis
5.1 On-Axis Source
The effects of diffraction due to slit and pupil masking at a wavelength of 2.5 mm are shown in the sequence of images in Figure 1. The images shown for an on-axis source are the telescope pupil image, the image at the IFU image slicer, this image seen through a single 0.1˛ wide slitlet, the pupil image at the pupil mirror, the masked pupil at the grating, and the image at the detector. The telescope diffraction rings are seen clearly, along with the smearing of the pupil images in the dispersion (horizontal) direction and the diffraction effect due to the finite lengths of the pupil mirrors and the grating on the final slit image at the detector. The latter effect is manifest as a faint slit diffraction pattern in the dispersion direction.
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Telescope Pupil |
Telescope Image |
Single Slitlet |
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Pupil Mirror |
Grating Pupil |
Image at Detector |
Figure 1: Pupil and image planes for an on-axis source at 2.5 mm, seen through a 0.1˛ wide slitlet with 46.4 mm ´ 90 mm grating.
5.2 Off-Axis Source
Objects of scientific interest will generally not be accurately centered in the NIFS IFU slitlets; most science objects will either be point sources distributed randomly across the field-of-view or will be extended. It is therefore necessary to examine diffraction effects as a function of the source position in an IFU slitlet.
The sequence of images shown in Figure 1 is repeated in Figure 2 for a source offset 0.05˛ from the slitlet center. This places the center of the Airy disk on the edge of the slitlet. Comparison of Figure 1 and Figure 2 shows that the distribution of light at the pupil mirror is broader for the off-axis source. This is to be expected because of the sharp discontinuity in the image plane at the slitlet edge. The same effect is seen when this pupil image is reimaged onto the grating. More severe masking of the pupil image by the finite extent of the grating then causes a more prominent slit diffraction pattern in the dispersion direction at the detector.
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Telescope Pupil |
Telescope Image |
Single Slitlet |
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Pupil Mirror |
Grating Pupil |
Image at Detector |
Figure 2: Pupil and image planes for a 0.05˛ off-axis source at 2.5 mm, seen through a 0.1˛ wide slitlet with 46.4 mm ´ 90 mm grating.
5.3 System Throughput
The broadening of the collimated beam relative to the geometrical beam size caused by diffraction will lead to light loss unless large optical elements are used in the collimated beam. The throughput degradation due to light loss at the pupil mirrors and grating has been calculated as a function of the physical grating length (including the projection factor) since this sets the scale of the collimated beam optics. Both on-axis and 0.05˛ off-axis point sources were considered because the light distribution at the pupil mirrors varies with the off-axis position of the source. The curves in Figure 3 and Figure 4 show the system throughput at a wavelength of 2.5 mm as a function of the physical length of the grating. This wavelength represents the worst case for diffraction losses in NIFS. The throughput rises more steeply with increasing grating length for the on-axis source because the pupil image is more centrally concentrated in this case. The system throughput reaches a maximum in both cases for gratings longer than ~ 113 mm. Beyond this length the throughput is set by the length of the pupil mirrors rather than by the length of the grating. For the 4.0 mm long pupil mirrors adopted here, it is clear from Figure 3 and Figure 4 that a grating length of ~ 60 mm provides an acceptable trade between system throughput degradation and optical complexity and expense.
Figure 3: System throughput at 2.5 mm due to diffraction losses for an on-axis point source.
Figure 4: System throughput at 2.5 mm due to diffraction losses for a point source offset 0.05˛ from the slitlet center.
5.4 Emission-Line Profile
Diffraction effects at the pupil images tend to produce wings on the profiles of point sources in the dispersion direction (Figure 1 and Figure 2). Extended sources will produce the same effect, with airglow from OH emission lines being the most problematic in this regard because of the extreme brightness of many of these lines compared to the faint source that NIFS will measure. The profiles of OH airglow lines have been modeled by considering the image profile at the detector of a source of uniform illumination. A uniform source is modeled by summing the contributions from twenty-one point sources that are equally spaced by 0.01˛ along a 0.2˛ long line in the image slicer plane perpendicular to and centered on the 0.1˛ wide slitlet. Since the phases of OH airglow emissions from different positions on the sky are uncorrelated (i.e., the emission is incoherent across the slitlet), light from each position in the slit must be propagated through the system independently. The image intensity at the detector is calculated for each slit position and co-added and summed along the slit image to produce the final OH emission-line profile.
OH emission-line profiles were calculated for grating lengths of 60 mm and 100 mm at a wavelength of 1.3 mm appropriate to science measurements of Ha at a redshift of z = 1. These profiles are shown in Figure 5 and Figure 6, respectively. The fringing seen in the wings of the profiles is probably due to numerical instabilities in the FFT at the Nyquist frequency. It is apparent that the attenuation of the signal more than ~ 3 pixels (~ 0.15˛) either side of the line center is a factor of > 660 for a 60 mm grating length and a factor of > 2500 for a 100 mm grating length.
Figure 5: OH emission-line profile at 1.3 mm for a grating length of 60 mm.
Figure 6: OH emission-line profile at 1.3 mm for a grating length of 100 mm.
ALTAIR will not deliver a perfect diffraction-limited image to NIFS. In fact, Strehl ratios of ~ 0.2, 0.4, and 0.6 are expected at J, H, and K, respectively. The program used to investigate diffraction in NIFS was originally written to model diffraction effects in an adaptive optics corrected coronagraph. Wavefront phase errors due to atmospheric turbulence are modeled using a series of Zernike polynomials. The effect of the ALTAIR AO system is modeled by applying a 90% reduction to the coefficients of the first 50 Zernike polynomials. This produced a Strehl ratio of ~0.3 for images at 1.3 mm on Gemini. This capability of the analysis program has been used to investigate the effects of only partial correction by the AO system.
When operated in this mode, the analysis program generates coefficients for the series of Zernike polynomials in a random way consistent with atmospheric turbulence. Each series of coefficients represents one realization of the atmospheric phase distortion, which produces a particular set of speckles in the image plane. A seeing-limited image is formed by adding together a large number of speckle images corresponding to different realizations of atmospheric turbulence. The OH line analysis was repeated by co-adding 20 such speckle images from an ensemble having a seeing full width at half maximum of 0.4˛. The results were insignificantly different from the diffraction-limited emission-line profiles in Figure 5 and Figure 6. This can be understood by realizing that each speckle image is comprised of several offset near-diffraction-limited images of the source. Offsets in the image plane are not transferred to the pupil plane, so the pupil image of a partially AO corrected extended source is similar (perhaps identical) to its diffraction-limited equivalent. Diffraction effects at the grating then produce similar emission-line profiles at the detector.
6 Conclusions
Spectrographs designed to take full advantage of adaptive optics systems will use slits comparable in width to the telescope diffraction-limit. Slit diffraction then broadens (i.e., speeds) the beam emerging from the slit and increases the size of the pupil image in the dispersion direction. The finite size of the collimated beam optics results in a throughput loss. Diffraction effects at the pupil image broaden the slit image formed at the detector.
NIFS will have 0.1˛ wide slits and 4 mm long pupil mirrors. A grating length of ~ 60 mm then offers an acceptable trade between throughput degradation and the complexity and expense of the collimated beam optics. The profiles of OH airglow lines will be slightly broadened by diffraction effects at the grating. However, OH lines at 1.3 mm will be attenuated by a factor of > 660 beyond ~ 3 pixels from the line center with a 60 mm grating. This is considered to be an acceptable level of OH line contamination of the dark inter-line wavelength regions.
Appendix B: List of Figures
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Figure 1a |
tel_mask_90_0.gif |
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foc_img_90_0.gif |
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foc_slit_90_0.gif |
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pup_img_90_0.gif |
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Figure
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gra_mirr_90_0.gif |
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Figure
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det_img_90_0.gif |
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Figure 2a |
tel_mask_90_5.gif |
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Figure 2b |
foc_img_90_5.gif |
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Figure 2c |
foc_slit_90_5.gif |
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Figure 2d |
pup_img_90_5.gif |
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Figure 2e |
gra_mirr_90_5.gif |
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Figure 2f |
det_img_90_5.gif |
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Figure 3 |
grat_eff_90_0.gif |
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Figure 4 |
grat_eff_90_5.gif |
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Figure 5 |
prof_det7.gif |
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Figure 6 |
prof_det8.gif |
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