Spatial Heterodyne Spectroscopy: An emerging technology for interference spectroscopy of diffuse airglow emissions

Transcription

1 Spatial Heterodyne Spectroscopy: An emerging technology for interference spectroscopy of diffuse airglow emissions E.J. Mierkiewicz a, F.L. Roesler a, J.M. Harlander b, R.J. Reynolds c, K.P. Jaehnig d a Dept. of Physics, Univ. of Wisconsin, 1150 University Ave., Madison, WI, USA 53706; b Dept. of Physics, St. Cloud State Univ., 720 Fourth Ave. S., St. Cloud, MN, USA 56301; c Dept. of Astronomy, Univ. of Wisconsin, 475 N Charter St., Madison, WI, USA 53706; d Space Astronomy Lab., Univ. of Wisconsin, 1150 University Ave., Madison, WI, USA ABSTRACT Spatial Heterodyne Spectroscopy (SHS) stands poised to play a significant role in ground-based aeronomy. In the basic SHS system, Fizeau fringes of wavenumber-dependent spatial frequency are produced by a Michelson interferometer modified by replacing the return mirrors with diffraction gratings; these fringes are recorded on a position sensitive detector and Fourier transformed to recover the spectrum over a limited spectral range centered at the Littrow wavenumber of the gratings. The system combines interferometric and field-widening gains in tandem to achieve 10,000-fold sensitivity gains compared to conventional grating instruments of similar size and resolving power. SHS systems also have relaxed flatness tolerances (20-50 times compared to Fabry-Perots) and do not require precision imaging to achieve diffraction-limited spectroscopic performance. Defects can largely be removed in data processing. This paper will briefly describe the SHS technique, and a newly fielded SHS for astrophysical application, which has also proved useful for the study of upper-atmospheric [OII] emission at 3727 Å. 1. THE SHS CONCEPT Interferometric spectroscopic instruments offer sensitivities typically 100 times those of conventional grating spectroscopic instruments of similar size in many applications. At the University of Wisconsin and St. Cloud State University the authors have been developing an unusual and novel interference spectroscopic technique called Spatial Heterodyne Spectroscopy (SHS). It is an interferometric Fourier transform technique, but unlike conventional Fourier transform spectroscopy (FTS) it requires no moving parts for obtaining a spectrum. Moreover it can be field-widened (also without moving parts) to provide additional gains of typically 100. As a net result, the SHS instrument can be made small and still achieve a level of performance equal or superior to grating instruments of practical dimensions. At the same time the SHS technique avoids many of the mechanical problems associated with conventional field-widened FTS techniques. At UV wavelengths SHS instruments are more practical than Fabry-Perot spectrometers due to their relaxed tolerances on element flatness (λ/2 compared with λ/100 for a Fabry-Perot), reduced sensitivity to coating absorption, and the ability to correct for interferometer defects in data analysis. In the basic spatial heterodyne spectrometer, 1 Fizeau fringes of wavenumber-dependent spatial frequency are produced by a modified Michelson interferometer in which the return mirrors are replaced by conventional blazed diffraction gratings (refer to Figure 1). For each wavelength in the wavefront entering the interferometer, two wavefronts exit with a wavelength-dependent crossing angle between them. This produces a superposition of Fizeau fringes with wavelength dependent spatial frequencies localized near the gratings. The fringes are recorded on a position sensitive detector and Fourier transformed to recover the spectrum. In this process, no element is mechanically scanned. The heterodyne concept is evoked by the fact that the dispersive elements may be tuned to place zero spatial frequency at a selected wavenumber σ o, where σ o is the Littrow wavenumber of the diffraction gratings (2σ o sin θ = m/d). For a system tuned to σ o, adjacent spectral elements σ o + δσ, σ o + 2δσ, σ o + nδσ produce 1,2,n-cycle spatial frequencies across the detector; refer to Figure 2. As each spectral element produces a unique spatial frequency at the detector, the Fourier transform of the recorded spatial frequencies provides the spectrum within a limited spectral range (determined by the detector sampling) about the heterodyne wavelength. As a

2 result high resolution spectra over a limited spectral range can be measured with modest requirements on the spatial resolution of the detector. The diffraction limited resolving power, R, of the grating system (the number of grooves, including both gratings, imaged on the detector) is achieved. If the pattern is imaged by N pixels, the total number of resolvable frequencies is N/2, giving a bandwidth of Nλ/2R; a filter blocks light outside this range. The field of view of the SHS system is characteristic of interferometric spectrometers (conventional Michelsons and Fabry-Perots), giving SHS systems a 100 fold gain in sensitivity for diffuse source spectroscopy over diffraction grating spectrometers of the same size and resolving power. Furthermore, field widening prisms can be placed in the arms of the interferometer which enable SHS instruments to view even larger fields of view. Gains associated with field widening are typically two orders of magnitude in solid angle over conventional interferometers (10 4 larger than diffraction grating spectrometers). 2 The prism apex angles are chosen so that from a geometrical optics point of view the gratings appear coincident. The geometrical path difference in the system is then near zero for a wide range of input angles resulting in a field of view much like a conventional Michelson at zero path difference. Aberrations introduced by the prisms ultimately limit the field of view, but not before large gains can be achieved in many applications. At R = 50, 000, angles up to ±5 deg can be used within the interferometer. A more detailed description including results of laboratory demonstrations of field widening an SHS appear in Ref. 3, 4. The SHS arrangement can be thought of as a Twyman-Green interferometer often used for testing of optical surfaces except that diffraction gratings replace the test and reference surfaces of the Twyman-Green. Grating figure errors, if present, distort the Fizeau fringe pattern. Since the gratings are imaged onto the detector, a calibration image in monochromatic light provides a measure of the grating figure errors that can be used in software to correct broad-band interferograms. Fringe distortions resulting from beamsplitter and prism figure errors and index of refraction inhomogeneities are corrected by the same calibration if these elements are of good quality over the area sampled by one spatial resolution element on the detector. Since these elements are nearly focused on the detector, the area that is sampled at each detector pixel is relatively small resulting in relaxed tolerances on both the flatness and homogeneity of the interferometer elements. This is to be contrasted with conventional interferometers where a single channel detector collects light over the full aperture of the critical optical components; figure errors in conventional interferometers result in a reduction in the contrast of the fringes and a reduced signal-to-noise ratio in the recovered spectrum. 2. THE [OII] SHS AND OBSERVATIONS We are currently using the SHS technique to measure the extremely faint [OII] λ3726, λ3729 emission lines from the warm (10,000 K) ionized component of our Galaxy s interstellar medium (ISM). These [OII] lines are a principal coolant for this wide spread, photoionized gas and are a potential tracer of variations in the gas temperature resulting from unidentified interstellar heating processes that appear to be acting within the Galaxy. In the winter of 2003 an [OII] spatial heterodyne spectrometer, with the sensitivity and resolving power required to observe variations in the [OII] emission intensity from the ISM, was installed at the university of Wisconsin s Pine Bluff Observatory (PBO), Pine Bluff, WI. The spectrometer is coupled to an all sky (Alt-Az) siderostat with a field of view (FOV) on the sky of 2 deg. Refer to Figure 3. Initial alignments were made using visible laser light while the critical adjustments were made at λ3727 using a thormium-neon hollow cathode discharge lamp. The PBO spatial heterodyne spectrometer employs diffraction gratings with a groove density of 600 grooves mm 1, fused silica transmitting elements, field-widening prisms, and a cryogenically cooled CCD detector. An interference filter with a 20 Å passband, centered near λ3725, is used as a prefilter in order to reduce photon noise due to the sky background. The aperture at the gratings is 3.5 cm 3.5 cm, while the field of view at the gratings is 14 deg. Table 1 lists the characteristics of the [OII] SHS system. The achieved resolving power of the PBO [OII] SHS system is 30, 000. An optical ray-trace of the [OII] SHS system is presented in Figure 4. Light from the siderostat enters an objective lens and is focused onto the interference filter. A lens near the filter images the objective at infinity to ensure that all spatial positions on the filter see the same angular cone of light. The image of the sky is wavelengths written as λ####, e.g., λ3727, are in units of Å

3 Table 1. The Pine Bluff Observatory (PBO) [OII] SHS system. PBO SHS Resolution 30, 000 (0.12 Å or 9.7 km/s) Bandpass 12 Å Grating Size 35 mm 35 mm Groove Density 600 grooves mm 1 FOV: sky 2 deg FOV: gratings 14 deg Exit Optics f/1 CCD QE at λ % CCD array (24µm pixels) collimated by a third lens and enters the interferometer. Light exiting the interferometer is imaged by an f/1 fused silica lens system that images the fringe localization plane onto the CCD detector. In this arrangement the sky is completely out of focus on the detector and as a result the system measures the average spectrum over the instrument s 2 deg field of view on the sky. Figure 5a shows an [OII] interferogram obtained with the PBO spatial heterodyne spectrometer in an 60 second integration on the North American Nebula (NAN). The CCD is binned 1 4 (i.e., pixels) in order to reduce the number of reads in the non-dispersive (i.e., y) direction. This sample interferogram has not been corrected for dark current (negligible in 60s), or flat fielded; hot pixels were removed using a sigma filter approach. Evident in the interferogram are two sinusoidal fringe patterns (one from each [OII] line) which are crossed due to a small but deliberate out-of-plane (y) tilt of one of the gratings. When such a tilt is introduced, fringes from wavelengths on opposite sides of Littrow are rotated in opposite directions; wavenumbers σ > σ o are rotated clockwise, while σ < σ o are rotated counter clockwise. In this example, Littrow was set approximately half-way between the two [OII] lines, hence the two fringe patterns appear to be crossed at approximately equal and opposite angles. In the analysis of the NAN spectrum, the central region of the interferogram was cropped (in order to avoid the edges of the grating), apodized with a Gaussian function, and a two-dimensional Fourier transform was applied; refer to Figure 5b for the resulting power spectrum. Note, apodization, combined with cropping of the interferogram, results in an achieved resolving power of 30, 000 (0.12 Å or 9.7 km/s). There are 481 (x) pixels within the cropped region interferogram, out of a possible 512 pixels if the full CCD array were used. The [OII] spectrum is obtained from the interferogram by taking a slice through its two-dimensional Fourier transform (i.e., power spectrum); refer to Figure 5c. The data in this analysis are oversampled by a factor of three by zero-padding the interferogram before transformation. With the current 3 oversampling, Littrow (i.e., zero spatial frequency) occurs at pixel 722 (indicated by a dotted line in Figure 5c). Wavelength calibration is obtained by using a cerium-neon (CeNe) hollow cathode calibration spectrum (refer to Figure 6a); the spectral interval per pixel in Figure 5c is Å. In Figure 5d the NAN spectrum is wavelength calibrated and corrected to account for the prefilter response function. The exit optics in the current [OII] SHS system limit the number of resolvable frequencies detectable by the CCD to a bandpass which is 12 Å wide. This effect is apparent in the Fourier transform of a continuum source presented in Figure 6b. Ordinarily the spectral shape of a continuum source viewed by an SHS system would be dominated by the prefilter. In this case the fwhm of the prefilter is 20 Å, but inspection of Figure 6b indicates a bandpass of 12 Å. High spatial frequencies are not fully resolved by the CCD, and hence the bandpass of the PBO [OII] SHS system is limited to 12 Å. As the science goals of the [OII] SHS system only require a ±2 Å range centered on λ3727, a 12 Å bandpass is more than sufficient. A narrower filter will be selected as a future upgrade to the [OII] SHS system in order to limit the background currently accepted by the [OII] system (which is not contributing any useful spectral information,

4 only noise); in addition, the central wavelength of this filter will be adjusted so that the peak transmission is centered on λ3727. In early first light tests of the [OII] SHS system at PBO, the daysky was observed in the spectral region near λ3727; refer to Figure 6c. Again, the spectral shape of Figure 6c is dominated by the prefilter and exit optics, but solar Fraunhofer features are also apparent in the spectrum. In Figure 6d the daysky spectrum has been corrected for the filter response by dividing by a single Gaussian fit to the Fourier transform of the continuum source (Figure 6c). In Figure 7 the daysky spectrum from the PBO [OII] SHS system (Figure 7c) is compared with the Kitt Peak National Solar Observatory s (KPNO) solar atlas (Figure 7a and Figure 7b). 5 Figure 7a is a plot of the KPNO solar atlas at its full resolving power. In Figure 7b, the KPNO atlas was convolved with a (0.12 Å) fwhm Gaussian in order to simulate the lower achieved resolving power of the PBO SHS system. There are subtle differences between Figures 7b and 7c, some of which may be attributed to the fact that the PBO SHS system is viewing daysky whereas the KPNO atlas is centered on the sun. Preliminary results from the PBO [OII] SHS system confirms the superb performance of the SHS technique for measurements of spatially extended faint emissions, including the first detection of diffuse [OII] emission extending out to 20 deg from the Galactic equator ([OII] intensities ranged from tens of rayleighs near the Galactic plane to less than one rayleigh at high latitudes). Figure 8a is a 3 hour average centered on a region of low galactic [OII] emission (i.e., an off direction). Virtually all emission in Figure 8a is terrestrial in origin. Figure 8b (solid line) is a 3 hour average of a number of target science directions ( 12 deg out of the plane); the dotted line in Figure 8b is an overplot of the 3 hour off direction (Figure 8a) for comparison. Figure 8c is the target regions minus the off direction (i.e., Figure 8a - 8b). This preliminary subtraction demonstrates the utility of the on-off technique in isolating faint galactic emission from a complicated terrestrial foreground. The remaining [OII] line profiles in Figure 8c show structure indicating emission along the lines of sight from both the local interstellar gas and more distant gas in the Perseus spiral arm (located 40 km/s to the blue of the local emission). The total [OII] emission in Figure 8c is 4 R. In the process of separating the airlgow features in our bandpass from the the galactic emission we realized that the lines we were fitting and removing from the middle of galactic [OII] emission were [OII] lines from the upper atmosphere. Thus we have a small but good quality database of the upper-atmospheric [OII] night glow emission doublet that could be expanded if warranted. We estimate the terrestrial [OII] night glow intensities to be in the range of R, subject to improved intensity calibration to be done later. The 3729/3727 line intensity ratio is about 0.43:1 for the atmospheric lines compared to about 1.5:1 observed for the ISM lines. Preliminary analysis indicates that the intensities of the terrestrial [OII] lines (but not obviously their ratios) vary together by about a factor of 2 or more over the course of our measurements on any night; this is well in excess of any measurement errors. The shadow heights (altitude where the line of sight intersects the earth s shadow) during these observations ranged between 1250 km and 7400 km. The intensity variation on a single night might be weakly correlated with shadow height, but shadow height doesnt seem to be the major parameter determining the intensity on any night, or time of night, unlike the familiar terrestrial Balmer α emission. The intensity observed during a night when the shadow height averaged 2100 km is nearly the same as on a night when the shadow height averaged 7200 km. On the different nights of observation the Ap index varied between 7 and 64. There is no obvious dependence on Ap, but we note that during the night when the shadow height was highest (7400 km) the ap was FUTURE DEVELOPMENTS Many problems in aeronomy require a resolving power near 300,000. We have recently completed a paper study and have concluded that it is possible to construct a compact SHS system which would be capable of daysky 6300 Å wind and temperature measurements at high resolving power. In addition to its small size and reduced optical tolerances, SHS systems are better suited for dealing with complicated backgrounds. A primary disadvantage of the SHS technique is due to multiplex noise which reduces its 100-fold throughput gain over a Fabry-Perot.

5 ACKNOWLEDGMENTS This work is supported at the University of Wisconsin by National Science Foundation grant AST , and at St. Cloud State University by National Science Foundation grant AST The Wisconsin H- Alpha Mapper is funded by the National Science Foundation. We acknowledge valuable contributions from our colleagues. In particular J.W. Percival, M. Haffner, G. Madsen, W. Harris, and S. Nossal. We would also like to acknowledge the contributions of four (now former) St. Cloud State University undergraduate students who participated in this project: Brent Williams, Marcel Goldschen, Dan Hooper, and Tom Dalton. Finally we also wish to thank the helpful staff of the McMath-Pierce Solar Telescope for their assistance during the [OII] prototype observations at Kitt Peak. REFERENCES 1. J. M. Harlander and F. L. Roesler, Spatial heterodyne spectroscopy: A novel interferometric technique for ground-based and space astronomy, in Astronomical Telescopes and Instrumentation for the 21st Century, Proc. SPIE 1235, p. 622, J. M. Harlander, Spatial Heterodyne Spectroscopy, interferometric performance at any wavelength without scanning, Ph.D. Thesis, University of Wisconsin-Madison, J. M. Harlander, R. J. Reynolds, and F. L. Roesler, Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths, ApJ 396, p. 730, J. M. Harlander, F. L. Roesler, J. Cardon, C. Englert, and R. R. Conway, Shimmer: A spatial heterodyne spectrometer for remote sensing of earth s middle atmosphere, Applied Optics 41, p. 1343, R. L. Kurucz, I. Furenlid, J. Brault, and L. Testerman, Solar flux atlas from 296 nm to 1300 nm, N.S.O. Atlas No. 1, Kitt Peak, AZ, 1984.

6 Transmitting SHS a) b) G incident wavefront G B.S.!! P 2 input A! G Input 1 2 exiting wavefronts B.S. Output x! G P 1 Imaging Detector x Figure 1. Left: Schematic diagram of the basic transmitting SHS system. Wavelength-dependent Fizeau fringes which result from crossed wavefronts 1 and 2 at the exit of the interferometer are recorded along the x-direction by a positionsensitive detector. Right: Optical breadboard of the prototype [OII] SHS system, with a layout corresponding to the schematic diagram at the left.

7 Figure 2. The heterodyne concept is evoked by the fact that the dispersive elements may be tuned to place zero spatial frequency at a selected wavenumber σ o, where σ o is the Littrow wavenumber of the diffraction gratings (2σ o sin θ = m/d). For a system tuned to σ o, adjacent spectral elements σ o + δσ, σ o + 2δσ, σ o + nδσ produce 1,2,n-cycle spatial frequencies across the detector. As each spectral element produces a unique spatial frequency, the Fourier transform of the recorded spatial frequencies provides the spectrum within a limited spectral range (determined by the detector sampling) about the heterodyne wavelength. (Figure is after Ref. 3).

8 Figure 3. Left: [OII] SHS system installed under the east port siderostat at Pine Bluff Observatory. Lower Right: Close up of the interferometer block; f/1 exit optics couple the interferometer to an LN2 cooled CCD.

9 11:41:18 Objective Interference Filter Collimator CCD Exit Optics Interferometer Positions: 1-2 O II SHS Scale: MM 20-Aug-01 Figure 4. Optical ray-trace of the [OII] SHS system. Light from the siderostat (not shown) enters an objective lens and is focused onto the interference filter. A lens near the filter images the objective at infinity to ensure that all spatial positions on the filter see the same angular cone of light. The image of the sky is collimated by a third lens and enters the interferometer. Light exiting the interferometer is imaged by an f/1 fused silica lens system that images the fringe localization plane onto the CCD detector.

10 a) y x b) c) d) Α Α pixel wavelength Figure 5. (5a) [OII] interferogram obtained with the PBO spatial heterodyne spectrometer from a 60 second integration on the North American Nebula (NAN). The CCD is binned 1 4 in order to reduce the number of reads in the nondispersive (i.e., y) direction. Evident in the interferogram are two sinusoidal fringe patterns (one from each [OII] line) which are crossed due to a small but deliberate out-of-plane (y) tilt of one of the gratings. In this example, Littrow was set approximately half-way between the two [OII] lines, hence the two fringe patterns appear to be crossed at approximately equal and opposite angles. The central region of the interferogram was cropped and apodized with a Gaussian function, and a two-dimensional Fourier transform was applied. (5b) The resulting power spectrum. The [OII] spectrum (5c) was obtained from the interferogram by taking a slice through its two-dimensional Fourier transform; the dotted line in the spectrum corresponds to zero spatial frequency (i.e., Littrow). (5d) Wavelength calibrated and filter corrected NAN spectrum (the [OII] emission from NAN in the 2 deg field of view is estimated to be 100 R).

11 a) Ne pix 733 c) Ce pix 441 Ne pix 160 pixel wavelength b) d) wavelength wavelength Figure 6. (6a) Wavelength calibration is obtained by using a cerium-neon (CeNe) hollow cathode calibration spectrum (the spectral interval per pixel is Å). The exit optics in the current [OII] SHS system limit the number of resolvable frequencies detectable by the CCD to a bandpass which is 12 Å wide. This effect is apparent in the Fourier transform of a continuum source presented in (6b). Ordinarily the spectral shape of a continuum source viewed by an SHS system would be dominated by the prefilter. In this case the fwhm of the prefilter is 20 Å, but inspection of (6b) indicates a bandpass of 12 Å. High spatial frequencies are not fully resolved by the CCD, and hence the bandpass of the PBO [OII] SHS system is limited to 12 Å. Dotted lines in (6b) indicate where the filter response is down by 70%. (6c) Daysky was observed in the spectral region near λ3727. (6d) Corrected daysky spectrum accounting for the filter response function (by division by a normalized single Gaussian fit to (6b)).

12 a) KPNO solar atlas b) KPNO solar atlas, at SHS resolving power c) SHS daysky spectrum, PBO wavelength Figure 7. Daysky spectrum from the PBO [OII] SHS system (7c) compared with the Kitt Peak National Solar Observatory s (KPNO) solar atlas 5 (7a and 7b). (7a) is a plot of the KPNO solar atlas at its full resolving power. In (7b), the KPNO atlas was convolved with a (0.12 Å) fwhm Gaussian to match the resolving power of the PBO SHS system. (7c) shows the measured daysky spectrum from PBO with the [OII] SHS system.

13 a) off region b) on + off c) on - off wavelength { { OII λ3726 OII λ3729 Orion+Perseus emission Figure 8. (8a) A 3 hour average centered on a region of low galactic [OII] emission (i.e., an off direction); virtually all emission is terrestrial in origin. (8b) (solid line) A 3 hour average of a number of target science directions ( 12 deg out of the plane); the dotted line is an overplot of the 3 hour off direction (8a) for comparison. (8c) is the difference between the target regions and the off direction (i.e., 8a - 8b), highlighting the diffuse [OII] emission from the ISM. (8c) show structure indicating emission along the lines of sight from both the local interstellar gas and more distant gas in the Perseus spiral arm (located 40 km/s to the blue of the local emission). The total [OII] emission in (8c) is 4 R.

14 Figure 9. Terrestrial [OII] night glow. Add Caption..