Document ID	Source	Title
SDN0003.02	RSAA	NIFS Functional and Performance Requirements Document
SDN0004.00	RSAA	NIFS Requirements Analysis
SDN0005.00	RSAA	NIFS Optical Requirements
SDN0005.28	RSAA	NIFS Optical Design
SPE-S-G0041	IGPO	Gemini System Error Budget Plan

3 Introduction

The Gemini Near-infrared Integral-Field Spectrograph (NIFS) will perform near-diffraction-limited imaging spectroscopy at near-infrared wavelengths. The NIFS Functional and Performance Requirements Document (FPRD; SDN0003.02) describes the instrument requirements. The overall specification for the instrument is described in SDN0004.00 (NIFS Requirements Analysis), and the specification for the optical design is further refined in SDN0005.00 (NIFS Optical Requirements). The NIFS optical design is described in SDN0005.28 (NIFS Optical Design). This document defines the error budget that specifies how image quality degradation is distributed among the various optical components.

4 Bottom-Up Error Budget

The procedures outlined in the Gemini System Error Budget Plan (Oschmann 1997, SPE-S-G0041) have been followed in defining a preliminary optical tolerance budget for the baseline concentric IFU optical design. Optical aberrations are specified in terms of RMS wavefront error in nm. The Strehl ratio, S, achieved is given by

where s is the RMS wavefront error in nm and l is the wavelength in nm, and the approximation is valid for Strehl ratios larger than ~0.2. The bottom-up error budget is defined assuming that all reflective elements use raw diamond-machined surfaces (no post-polishing) with an RMS surface error of 20 nm. The associated wavefront error is doubled on reflection. Commercial transmissive elements (i.e., the cryostat window and the ZnSe camera lens) are assumed to have a RMS figure error of l/30 in the visible or ~ 20 nm. Transmissive elements manufactured in the RSAA Optical Workshop can be tested to an RMS accuracy of ~ l/30 (~ l/8 p-v). We adopt this figure error for the camera lenses, assuming they will be manufactured at RSAA. The order sorting filters have been specified to have a l/4 flatness at the central wavelength of the filter (i.e., ~ 1.6 mm). The grating is assigned an arbitrarily higher figure error due to the replication process. Different optical elements contribute to wavefront errors at the detector in different ways (e.g., an element at a pupil has more effect than an element at a focus). A detailed sensitivity analysis has not been performed yet. Instead, we assume that figure errors contribute to wavefront errors in proportion to the fractional area of the element illuminated by the beam. The concentric IFU optical design produces a RMS wavefront error at the detector of ~ 30 nm. This ignores the complicating effects of enlarged pupil sizes due to slit diffraction. The error budget includes an allowance for overall optical alignment of l/10 in the visible or ~ 60 nm. The individual RMS wavefront errors are combined to form the RSS sum of 129 nm listed in Table 1. This is slightly larger than the 124 nm nominal allocation to the science instrument in the Gemini System Error Budget Plan. The expects diamond-machining figure error will be better quantified through consultation with suppliers.

Table 1: Optical Tolerance Budget for the Concentric IFU Design

Component	RMS Figure Error		RMS Wavefront Error
	Quality	(nm)	(nm)

Cryostat Window	l/30 (vis)	20	2
Pick-Off Mirror	Diamond machined	20	10
F/# Converter Mirror	Diamond machined	20	30
Cold Stop Mirror	Diamond machined	20	40
Filter	l/4 (IR)	400	10
Fold 1 Mirror	Diamond machined	20	4
Fold 2 Mirror	Diamond machined	20	4
Fold 3 Mirror	Diamond machined	20	4
Image Slicer Mirror	Diamond machined	20	0
Pupil Mirror Array Mirror	Diamond machined	20	40
Field Mirror Array Mirror	Diamond machined	20	0
Fold 4 Mirror	Diamond machined	20	4
Collimator Mirror	Diamond machined	20	40
Fold 5 Mirror	Diamond machined	20	40
Collimator Corrector Lens	l/30 (vis)	20	20
Grating	Replicated	25	50
Camera Lens 1	l/30 (vis)	20	20
Camera Lens 2	l/30 (vis)	20	20
Camera Lens 3	l/30 (vis)	20	20
Camera Lens 4	l/30 (vis)	20	12
Camera Lens 5	l/30 (vis)	20	6

Optical Design			30
Optical Alignment			60
OIWFS Stability			20

RSS TOTAL			129

5 Top-Down Error Budget

A top-down optical error budget can be defined using the general scaling (Oschmann 1997, SPE-S-G0041) that a 50 nm RMS wavefront error corresponds approximately to a 0.01² degradation in 50% encircled energy diameter at 2.2 mm[1]. Spot diagrams for the concentric IFU design, including diffraction effects, place 90% of the light within one 0.04² pixel (NIFS Optical Design, SDN0005.28). Manufacturing tolerances and alignment errors may degrade this to 50% encircled energy within 0.04², which is converted to a RMS wavefront error of ~ 200 nm using the general scaling approximation. Both the bottom-up and the top-down optical tolerance estimates suggest that image qualities suitable for the near diffraction-limited sampling of NIFS can be achieved with routine, high quality optical surfaces and alignment procedures.

6 Flexure

The NIFS FPRD (SDN0003.02) specifies a flexure between the OIWFS and the science detector of < 0.1 pixel/hr, i.e., < 0.004²/hr. This is equated to a wavefront error of ~ 20 nm/hr using the general scaling relation. This tracking error makes little difference to either tolerance estimate, but is included in the bottom-up RSS total in Table 1.

[1] We adopt 50 nm RMS wavefront error (Oschmann 1999, priv. comm.) rather than the 100 nm quoted in Oschmann 1997, SPE-S-G0041.