This document describes the nature of fringing effects in the science detector of the Gemini Near-infrared Integral-Field Spectrograph (NIFS) and the extent to which these fringing effects can be corrected through division by flatfield frames.

2 Applicable Documents

Document ID	Source	Title
SDN0003.02	RSAA	NIFS Functional and Performance Requirements Document
SDN0005.21	RSAA	NIFS Grating Selection

3 Introduction

The Gemini Near-infrared Integral-Field Spectrograph (NIFS) will use a 2048´2048 HAWAII-2 detector manufactured by the Rockwell Science Center. Fringing in this detector due to optical interference will impose a modulation on the measured spectrum. In principle, this modulation can be corrected through division by a flatfield frame. However, any misalignment between the science frame and the flatfield frame will result in imperfect correction of the fringing pattern. The nature of the fringing pattern and the extent to which it can be corrected are the subjects of this document.

4 Physical Nature of Fringing

HAWAII-2 PACE detectors are manufactured by depositing the HgCdTe detector layer on a sapphire substrate. The science field is viewed through this substrate. Multiple reflections within the sapphire substrate cause optical interference which imposes a modulation on the measured light intensity. Being a spectrograph, NIFS will illuminate each pixel of the detector in the dispersion direction with light of different wavelengths. To first order, the fringing pattern can be considered to be caused by light of different wavelengths interfering at normal incidence in a layer of constant thickness. Light at different wavelengths actually originates from the grating pupil so the chief rays actually strike the detector at incident angles of up to ~ 3.6º. This causes a slight deviation from the first order pattern.

The wavelength of light focusing on each detector pixels is given by the grating equation

where m is the grating order, a is the grating groove density in l/mm, a is the incident angle at the grating, and b is the diffracted angle at the grating. All NIFS gratings work in first order (NIFS Grating Selection, SDN0005.21). The incident angle and on-axis reflected angle, b₀, can be expressed in terms of the grating angle (q) and the Ebert angle (f) as

The Ebert angle in NIFS is f = 30º, and the operating angles for the NIFS gratings are listed in Table 1 (NIFS Grating Selection, SDN0005.21). The diffracted angle corresponding to each detector pixel is defined geometrically by the camera focal length of 288 mm and the detector pixel size of 18 mm.

Light under-going multiple reflections in the sapphire substrate will constructively interfere when the optical path difference between adjacent transmitted beams is an integral number of wavelengths. This occurs when

where m is now the interference order, n is the refractive index of the sapphire substrate (~1.74), d is the thickness of the sapphire substrate, g' is the incident angle within the sapphire substrate, and n' is the refractive index in the HgCdTe detector material. We have no data on the refractive index of HgCdTe at near-infrared wavelengths, but this is of little consequence because the incident angles, g' are small. The analysis is simplified by assuming that n' = 1.0. The interference equation then reduces to the familiar Fabry-Perot equation

Constructive interference occurs at integral values of m and destructive interference occurs at half-integral values of m.

5 Fringe Period

Fringing effects in NIFS have been modeled by calculating the interference order, m, across the detector for each of the NIFS gratings (Figure 1 to Figure 5). A sapphire substrate thickness of 0.015 inches has been assumed. The average fringe periods in pixels for each grating are listed in Table 1. Hodapp et al. (1996, New Astr, 1, 177) report a fringing period with KSPEC of ~ 9 pixels at K. KSPEC disperses the K band over 1024 pixels, so produces a fringing period in pixels of approximately half that of NIFS, as we predict (Table 1).

Figure 1: Interference order vs wavelength for the Z grating.

Figure 2: Interference order vs wavelength for the J grating.

Figure 3: Interference order vs wavelength for the H grating.

Figure 4: Interference order vs wavelength for the Ks grating.

Figure 5: Interference order vs wavelength for the Kl grating.

Table 1: NIFS Grating Parameters

Grating	Groove Density (l/mm)	Grating Angle (deg)	Wavelength (mm)	Range (mm)	Fringe Spacing (pixels)

Z	600	19.0	1.05	0.94-1.15	7.9
J	600	22.8	1.25	1.15-1.35	11.2
H	400	19.9	1.65	1.49-1.80	12.9
Ks	300	19.5	2.15	1.95-2.36	16.5
Kl	300	20.8	2.29	2.09-2.50	18.8

6 Fringe Correction

In principle, the modulation due to fringing can be corrected through division by a suitable flatfield frame. In practice, it is difficult to ensure that the flatfield lamp illuminates the slit of integral-field unit (IFU), in the case of NIFS, in exactly the same way as does the science object. In addition, small amounts of flexure between the science exposure and the flatfield exposure will cause incomplete cancellation.

The effect of flexure on fringing correction has been simulated by dividing a model fringe pattern by a shifted flatfield spectrum. The maximum peak-to-valley amplitude in the corrected spectrum is listed in Table 2 to Table 6 for each of the NIFS gratings. NIFS is required to have a flexure of <0.1 pixel per 15º change in attitude (NIFS Functional and Performance Requirements Document, SDN0003.02). We may expect a flexure of ~ 0.2 pixels between a flatfield frame taken at twilight and a typical science frame. Hodapp et al. (1996, New Astr, 1, 177) report a peak-to-valley modulation of ~ 10% in the uncorrected fringe pattern with KSPEC and a HAWAII-1 array. If the HAWAII-2 array is similar, we expect a maximum peak-to-valley variation in corrected NIFS spectra due to flexure of ~ 1.3%, 0.9%, 0.8%, 0.6%, and 0.5% with the Z, J, H, Ks, and Kl gratings, respectively. Illumination differences between the flatfield and science frames may increase these residuals.

Table 2: Percentage residual maximum p-v modulation for Z grating

% Fringe Amplitude (p-v)	Flexure shift (pixels)
% Fringe Amplitude (p-v)	0.1	0.2	0.5	1.0	1.5	2.0

100	11.8	22.5	53.5	99.0	139.5	177.2
80	8.0	15.4	37.1	69.9	99.2	126.7
60	5.2	10.1	24.7	47.2	67.7	87.2
40	3.0	6.0	14.8	28.7	41.8	54.3
20	1.4	2.7	6.7	13.3	19.6	25.8
10	0.7	1.3	3.2	6.4	9.5	12.6

Table 3: Percentage residual maximum p-v modulation for J grating

% Fringe Amplitude (p-v)	Flexure shift (pixels)
% Fringe Amplitude (p-v)	0.1	0.2	0.5	1.0	1.5	2.0

100	8.0	15.5	37.6	69.8	100.1	126.7
80	5.4	10.5	25.9	48.8	70.6	90.1
60	3.5	6.9	17.0	32.7	47.7	61.4
40	2.1	4.1	10.1	19.7	29.1	37.8
20	0.9	1.8	4.6	9.0	13.4	17.7
10	0.4	0.9	2.2	4.3	6.5	8.6

Table 4: Percentage residual maximum p-v modulation for H grating

% Fringe Amplitude (p-v)	Flexure shift (pixels)
% Fringe Amplitude (p-v)	0.1	0.2	0.5	1.0	1.5	2.0

100	7.1	14.2	33.8	63.1	90.1	114.8
80	4.8	9.6	23.2	44.1	63.5	81.6
60	3.1	6.2	15.2	29.4	42.7	55.5
40	1.8	3.7	9.0	17.7	26.0	34.1
20	0.8	1.7	4.1	8.1	12.0	15.8
10	0.4	0.8	2.0	3.9	5.8	7.7

Table 5: Percentage residual maximum p-v modulation for Ks grating

% Fringe Amplitude (p-v)	Flexure shift (pixels)
% Fringe Amplitude (p-v)	0.1	0.2	0.5	1.0	1.5	2.0

100	5.5	11.0	26.7	50.7	72.8	93.4
80	3.7	7.5	18.3	35.2	51.1	66.0
60	2.4	4.9	12.0	23.4	34.3	44.6
40	1.4	2.9	7.1	14.0	20.7	27.1
20	0.6	1.3	3.2	6.4	9.5	12.5
10	0.3	0.6	1.5	3.0	4.6	6.0

Table 6: Percentage residual maximum p-v modulation for Kl grating

% Fringe Amplitude (p-v)	Flexure shift (pixels)
% Fringe Amplitude (p-v)	0.1	0.2	0.5	1.0	1.5	2.0

100	4.9	9.7	23.1	44.7	63.4	82.9
80	3.3	6.6	15.9	30.9	44.6	58.2
60	2.1	4.3	10.4	20.4	29.9	39.1
40	1.3	2.5	6.2	12.2	18.0	23.7
20	0.6	1.1	2.8	5.5	8.3	10.9
10	0.3	0.5	1.3	2.7	4.0	5.3

Appendix A: List of Figures

Figure 1	fringing_z.gif
Figure 2	fringing_j.gif
Figure 3	fringing_h.gif
Figure 4	fringing_ks.gif
Figure 5	fringing_kl.gif