Operation of an all-reflection, broadband, spatial heterodyne spectrometer (SHS) is reported. This Mark 2 SHS is constructed using a custom diffraction grating and other standard optical components. The custom grating is coarse (18 grooves/mm), with a symmetric blaze that allows its simultaneous use as dispersing element and beam splitter and combiner. The grating is combined with a plane mirror and a roof mirror to form a very stable ring interferometer which has been used successfully in earlier narrowband SHS designs. Fringes from the extra grating orders in the main blaze envelope are unexpectedly found to combine constructively with the desired primary fringes of the interferometer. Elimination of ambiguity between wavelengths above and below blaze in a given order, and order separation are demonstrated using a small tilt of the plane mirror about an axis in the plane of the figure. Coverage of a factor of four in wavelength in a single CCD frame is demonstrated.
© 2010 OSA
Interference spectrometers, such as scanning Fourier transform spectrometers (FTSs) and Fabry-Perot spectrometers (FPs), offer many well-known advantages over conventional diffraction grating instruments, particularly at high spectral resolving power when sensitivity and size are important considerations. However, interference spectrometers typically have demanding alignment, wavefront flatness and stability requirements, especially at short wavelengths. In order to extend the advantages of interference spectroscopy into the ultra-violet we have been developing a family of spatial heterodyne spectrometer (SHS) instruments. Spatial heterodyne spectroscopy is a Fourier transform technique whereby a static two-beam interferometer produces wavelength-dependent Fizeau fringes that are recorded on an imaging detector [1–4]. The recorded fringe pattern is then Fourier Transformed to recover the spectrum. We have recently demonstrated  a multi-order SHS instrument based on a transmitting beamsplitter (hereafter call the Mark 1 SHS) that uses conventional Echelle gratings in each arm to simultaneously record over a factor of four in wavelength. At short wavelengths this instrument is limited by a transmitting beampslitter/compensator plate. SHS instruments can be built in an all-reflection configuration , but to date an all-reflection SHS has been demonstrated simultaneously only over a limited spectral band (a tunable all-reflection SHS is described in ). In this letter we describe an all-reflection broad-band SHS instrument (hereafter called the Mark 2 SHS) that uses a symmetrically blazed high-order diffraction grating as the beamsplitter and combiner. The Mark 2 simultaneously records multiple orders of interference which significantly extends its spectral range.
The Mark 2 SHS is based on a common-path interferometer design that uses a normal-incidence diffraction grating as the beam splitter/beam combiner and the dispersive element. Figure 1 is a schematic diagram of the system. Light incident normally on the diffraction grating diffracts symmetrically into two equal and opposite orders, one of which circulates clockwise and the other counterclockwise around the triangular path shown in Fig. 1. A roof mirror with apex in the plane of the figure translates the counter-propagating beams into the plane of the figure such that the top half of the grating is used as the beam splitter and the bottom half is the beam combiner. Use of the roof mirror prevents overlap of the incoming and outgoing beams. To obtain broad spectral coverage a low line density (~18 lines mm−1) normal incidence diffraction grating was used to produce multiple orders of interference simultaneously. The custom triangular-groove symmetrically-blazed diffraction grating was fabricated by Bach Research of Boulder CO. Multiple orders of diffraction, each producing an interferogram are measured simultaneously. To separate these orders the plane mirror in the interferometer is tilted slightly so as to produce a low spectral resolution fringe pattern perpendicular to the plane of Fig. 1. This, in addition to the high spectral resolution fringe pattern provided by the diffraction grating results in a two-dimensional fringe pattern that when Fourier transformed in 2D results in a spectrum much like a cross-dispersed Echelle spectrograph with high spectral resolution in one dimension while the other dimension provides order separation. The free spectral range in any given order is determined by the grating blaze efficiency so with proper choice of grating and detector sampling, continuous spectral coverage without aliasing can be achieved (see reference  for a detailed discussion).
Figure 2 is a photograph of the Mark 2 instrument with superposed rays to show the beam paths. Collimated light is incident from the left in the figure (the yellow ray indicates the incident chief ray). The interferometer is on the right half of the figure and consists of the diffraction grating beamsplitter/combiner, the roof mirror and a fold mirror. For clarity only rays along the optical axis have been drawn. A collimating mirror (M1 in Fig. 1) is to the left of the figure and not shown. The top half of the grating is the beam splitter and the bottom half the beam combiner. The roof mirror has its apex along the instrument mid-plane and thus serves to translate both counter-circulating beams from the top to the bottom half-plane. After recombining at the grating light exits the interferometer below and parallel to the incident beam and, following a simple fold mirror, enters an Offner imaging system. The Offner (on the left half of Fig. 2) is a three-mirror all-reflective, telecentric, imaging system with unit magnification and no third-order aberrations . The Offner which replaces mirror M2 in Fig. 1, reimages the fringes generated inside the interferometer onto the CCD detector (not shown). Table 1 shows the design parameters of the Mark 2 instrument.
Tests of the Mark 2 instrument were performed using a low pressure mercury discharge (germicidal) lamp. A premonochromator just before the collimator input aperture was optionally used to isolate a narrow spectral region (one or a few emission lines) during initial alignment and testing of the Mark 2. Figure 3 shows a section of the 2D Fourier transform of an interferogram obtained using the germicidal mercury (Hg) lamp with the premonochromator in zero order so all wavelengths emitted by the lamp entered the SHS. The interferogram was from an 800 second integration. Zero fringe frequency in the high resolution direction for the multiple grating orders is along the vertical centerline with fractional order between 0 and 0.5 to the right and −0.5 and 0.0 to the left of center. The axes labels show the number of fringes for each of the lines in each dimension. The intensity scale has been set to saturate the brightest lines in order to bring out the weaker ones. The wavelengths of the Hg lines identified with lower case letters in Fig. 3 along with their order number and number of fringes in each dimension are indicated in Table 2.
Figure 4 shows plots of line shapes obtained for four of the Hg lines from the same interferogram of the germicidal lamp. Each plot is a three column sum of 100 pixels in a row near the corresponding Hg line. Titles on each subplot refer to the familiar Hg wavelengths in nm units for selected strong Hg lines including λ = 579 nm, 546 nm, 436 nm, and 254 nm. The intensity of each line has been scaled from the raw, uncalibrated, spectral intensity. Since the Hg spectra were all obtained from the same interferogram, each Hg subplot has approximately the same noise on an absolute scale. Emission lines from low-pressure germicidal lamps have resolvable isotopic and hyperfine structure, especially on the 254 nm
Hg resonance line. These strong Hg lines, especially the resonance line, are not optically thin in germicidal lamps.
The data of Figs. 3 and 4 demonstrate coverage from the 254 nm Hg resonance line to the Hg line at 1014 nm in a single CCD frame. The resolving power of the instrument is best evaluated from the narrow Hg lines at 577 nm. Since the 577 nm and 579 nm lines are both in the same grating order (22nd), the spectral interval per pixel can be determined by dividing the difference in wavenumber of the two lines by the their horizontal pixel separation. The result gives a spectral sampling of 0.812 cm−1 per pixel. The central lobe of the 579 nm line in Fig. 4 is approximately 3 pixels wide in the final spectrum from the apodized and transformed interferogram. The limit of resolution is then 𝛿𝜎⋍3 * 0.812 cm−1 or 2.4 cm−1. The limit of resolution is constant in wavenumbers in FTS data, while the resolving power at a specific wavenumber is proportional to that wavenumber. The resolving power (R = 𝜎/𝛿𝜎) at 17,300 cm−1 is 7100.
The resolution limit achieved by the Mark 2 SHS is almost 3 times larger (worse) than the design value (see Table 1). A detailed analysis, which is beyond the scope of this paper, indicates that the reduction in spectral resolving power is due to additional fringe patterns with slightly different frequencies caused by cross interferences from orders above and below those indicated in Table 2 but still inside the blaze peak of the diffraction grating (see reference  for a detailed description of cross order interference). A standard echelle grating has a facet width that yields an angular blaze envelope encompassing one grating order at perfect Littrow and two orders otherwise. The narrower facets of the beamsplitter grating results in two or three grating orders inside the angular blaze envelope. The majority of the cross-order interferences fall within one or two spectral resolution elements of the main peak which is the right magnitude to explain the broadening of the observed line widths. Analysis of cross order interferences also suggests that the side lobes evident in the line shapes are due to high frequency fringe patterns caused by interferences between grating orders other than the primary order. These interferences are at frequencies above Nyquist’s limit and are aliased to produce the satellite peaks at approximately +/−5 and +/−12 pixels away from the primary peak.
Although the line shapes are wider than expected and contain side lobes, surprisingly high fringe formation efficiency measurements were obtained using the technique described in . Effective fringe efficiencies for the 546 nm line are around 88%. This suggests that even though the cross order interferences affect the instrument profile, the fringe patterns are in phase with the main fringe pattern which results in high contrast fringes. In practice, this means that the integrated signal under each line (including the side lobes) represents almost all of the incident optical power.
This work was supported by NASA grants NNX08AQ09G and NNZ07AU0G.
References and links
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