Abstract

For applications where only moderate spectral resolution is required, static Fourier transform infrared spectrometers (sFTS) offer a comparatively cost-effective alternative to classical scanning instruments. In this paper, we present an sFTS based on a single-mirror interferometer using only standard optical components and an uncooled microbolometer array. Because the instrument features concave mirrors rather than lenses, dispersion effects can be minimized. This enables broadband operation in the mid-infrared range from 2800cm1 to 600cm1 at a spectral resolution of 12cm1. In addition, the design guarantees comparatively high light throughput and can potentially be designed for increased temperature stability. Alongside a simulation of the temperature- and wavenumber-dependent behavior of the system, we provide a proof of principle of the proposed design by means of experimental results.

© 2019 Optical Society of America

1. INTRODUCTION

Scanning Fourier transform infrared (FTIR) spectrometers today represent the standard instrument for quantitative and qualitative laboratory analysis of gases, fluids, and solids in the mid-infrared spectral range [1], especially if moderate spectral resolution is sufficient for the application; however, static Fourier transform spectrometers (sFTS) can offer a viable alternative to these conventional systems, as they comprise no moving parts and therefore can be built in a cost-effective and, at the same time, rugged way. For the mid-infrared spectral range, so-called source-doubling interferometers creating a pair of divergent light sources in front of a Fourier optic emerged advantageous, as they work with light sources independent of their sizes and hence offer a comparatively high light throughput [2]. While various designs have been proposed, using birefringent [3], spatially modulated prism [4], or common-path interferometers [59], this paper presents a novel broadband static Fourier transform spectrometer (bsFTS) based on a single-mirror interferometer, as described in [10,11].

Dispersion effects can have a negative impact on the performance of these systems, especially when using a lens as a Fourier optic, as the focal length and therefore the contrast as well as the sampling frequency of the interferogram are then both wavelength- and temperature-dependent [12,13]. Although correction algorithms exist [13], the lens typically has to be temperature-controlled and still leads to a loss of spectral bandwidth. Setups comprising concave mirrors as Fourier optics have been proposed; however, these systems either work with narrowband light sources or large focal lengths leading to low spectral resolutions [5,7,9] or include customized and hence comparatively expensive mirror assemblies [4,8].

Therefore, in this paper, we present a bsFTS based on a single-mirror interferometer, where the Fourier lens is replaced by a spherical concave mirror to eliminate dispersion effects. The system works in the mid-infrared spectral range from 3.6 μm to 17 μm, respectively, from 2800cm1 to 600cm1at a spectral resolution of about 12cm1, while only off-the-shelf mirrors, a beam splitter, and an uncooled broadband microbolometer array are used. As no lenses are included in the spectrometer, its performance is potentially independent of temperature and wavenumber. In addition, high signal-to-noise ratios (SNR) can be achieved, as the system shows in principle no internal light losses, and the second detector dimension can be used for averaging. As for any sFTS, measurement speed is only limited by the detector readout frequency and thermal time constant [14]. With the currently used detector, measurement rates up to 25 Hz can be achieved.

At first, we introduce relevant fundamentals of static single-mirror Fourier spectrometers and the source-doubling principle. After a simulation of the wavenumber and temperature-dependent behavior of both lens- and mirror-based sFTS, we present our experimental setup and provide a proof of principle of the proposed concept by means of different measurement results.

2. SINGLE-MIRROR FOURIER TRANSFORM SPECTROMETERS

Before describing the proposed setup in detail, we give a brief overview of static single-mirror Fourier transform spectrometers (sSMFTS) as well as the source-doubling principle in general. Furthermore, we characterize the temperature and wavelength dependence of different Fourier optics.

A. Basic Principle of sSMFTS

Figure 1 shows the basic design principle of static single-mirror Fourier transform spectrometers. Light from an extended light source hits a beam splitter with thickness Tbs at point A, where it is split into one part being transmitted to point B1 and another part being reflected twice by the beam splitter and a plane mirror to point B2. For the sake of convenience, only the central rays of the light source are indicated here. In that way, the two central rays are separated by a distance sQ in front of a Fourier lens with focal length fF. Because the refractive index nbs of the beam splitter is considerably larger than that of the surrounding medium ns, the optical path lengths from A to B1 and from A to B2 can be matched by a suitable choice of the distance dbspm between the beam splitter and plane mirror. Eventually, the Fourier lens collimates the wave fronts of the two interferometer arms onto its focal plane, where the resulting interference pattern is captured by a 2D microbolometer array.

 

Fig. 1. Design principle of a static single-mirror Fourier transform spectrometer [10].

Download Full Size | PPT Slide | PDF

The interferogram I(x,y) formed on the 2D detector array is then given by Eq. (1), where S(ν˜) is the light source spectrum and B(ν˜) is the wavenumber-dependent instrument response function, including optics and detector characteristics. The horizontal position along the detector array is denoted by x, the vertical position by y:

I(x,y)=0S(ν˜)B(ν˜){1+cos(2πν˜(xsQfF+Δxnonlin(x,y)))}dν˜.
The optical path difference consists of a linear part and a nonlinear part Δxnonlin(x,y), the latter of which can be determined using a simple ray-tracing method, according to [10]. Figure 2 shows a typical pattern of optical path differences generated by a single-mirror interferometer on a 2D detector array. It is obvious that the main modulation of the optical path differences (OPD) occurs along the x axis, which is therefore referred to as the interferogram axis. Due to the astigmatism induced by the beam splitter, the lines of identical path differences as marked in the drawing are slightly curved along the y axis. This effect is described in detail in [10]. Nevertheless, it is possible to average along the y axis in order to increase the SNR without time averaging. This is therefore referred to as averaging axis. As depicted here, typically the zero path difference, where the midpeak occurs, is shifted slightly to one side of the detector to increase the maximum optical path difference OPDmax on the detector and therefore the spectral resolution of the system. After averaging the 2D image and thereby obtaining a 1D interferogram, the light source spectrum is finally reconstructed by applying a nonuniform Fourier transform [15]. As a matter of principle, according to Eq. (2), a trade-off must always be made between spectral resolution Δν˜ and maximum resolvable wavenumber:
Δν˜=1OPDmax2·ν˜maxgm·Nx.
Here, Nx denotes the number of pixels in the x direction, and gm0.5 describes the position of the midpeak on the detector, with gm=0.5 being the symmetrical position. The maximum resolvable wavenumber can also be expressed using the Nyquist theorem, according to Eq. (3). In this case, ppix describes the pixel pitch of the detector used:
ν˜maxfF2·sQ·ppix.

 

Fig. 2. Typical pattern of optical path differences generated by a single-mirror interferometer. The main path difference modulation occurs along the x axis. As indicated, the signal can be averaged along the curved lines of equal optical path difference along the y axis.

Download Full Size | PPT Slide | PDF

B. Source-Doubling Principle and Characteristics of Fourier Lenses

The sSMFTS principle can also be illustrated, as shown in Fig. 3. In this virtual source model, the two interferometer arms are represented as two separate divergent light sources V1 and V2, emitting spherical wave fronts. A Fourier lens, typically made of germanium, then collimates and tilts the wave fronts onto a detector array and thus creates an interference pattern. This is often referred to as source-doubling principle. As indicated in this depiction, the horizontal separation of the virtual sources sQ(λ,T) as well as the focal length of the Fourier lens fF(λ,T) depend on both wavelength λ and temperature T. Here, the former can be calculated using Eq. (4), with the variables being defined in Fig. 1. This approach assumes that the main effect on the distance between the virtual sources is the change in the refractive index of the beam splitter and that temperature-related expansions of the assembly and components can be neglected in a first approximation. Furthermore, it is assumed that the refractive index of the surrounding medium, in most cases air, exhibits minor changes with temperature and wavelength variations [10]:

sQ(λ,T)=dbspm+Tbs·(ns·sin(π4arcsin(nsnbs(λ,T)·2))1(nsnbs(λ,T)·2)2).
Similarly, expecting the change in focal length being rather caused by the change of the refractive index than the material expansion, we can calculate the focal shift ΔfF(λ,T) of the Fourier lens as a function of the design focal length fF,des and the design refractive index ndes of the lens, according to Eq. (5):
ΔfF(λ,T)=fF,des·ndesn(λ,T)n(λ,T)1.
Thereby, the wavelength and temperature-dependent refractive index n(λ,T) of Germanium can be calculated using Eq. (6) considering the Sellmeier coefficients from [16]:
n(λ,T)=(A+Bλ2(λ2C)+Dλ2(λ2E))1/2.
With the dependencies introduced above, it is now possible to calculate the temperature and wavenumber-dependent behavior of a typical spectrometer configuration. For the calculations carried out here, the design wavenumber is set to 943cm1 and the design temperature to 25° m. As for the latter measurement setup, we use a zinc selenide (ZnSe) beam splitter with a thickness of 3.1 mm and a germanium Fourier lens with a focal length of 75 mm. The radius of the extended light source is set to 1 mm, and the separation of the virtual sources amounts to 6.6 mm for the design values.

 

Fig. 3. Temperature- and wavelength-dependent virtual source model of a static single-mirror Fourier transform spectrometer.

Download Full Size | PPT Slide | PDF

In principle, two main effects can be observed in Fig. 4: different Michelson contrasts depending on wavenumber and temperature as well as a shift of the wavenumber axis in the spectrum. The former is mainly caused by the shift of the focal plane and may lead to quantitative measurement errors and a limitation of the spectral range. We illustrate this effect by simulating the ideal Michelson contrast over the relevant spectral and temperature range using the method from [12]. As can be seen in Fig. 4(a), the Michelson contrast decreases with the increasing wavenumber. Note that this effect becomes greater with shorter focal lengths, as indicated by dashed lines, as well as with larger light sources, and therefore somewhat limits the maximum spectral resolution and light throughput of the system [12]. Here, effects such as aberrations of the Fourier lens or detector characteristics are not considered, and an ideal linear interference pattern is assumed.

 

Fig. 4. (a) Simulation of the Michelson contrast for typical lens-based spectrometer configurations. Solid lines indicate a focal length of 75 mm, dashed lines a focal length of 40 mm. The radius of the light source is set to 1 mm. (b) Simulation of the wavenumber shift due to a changing distance between the virtual sources and a varying focal length of the Fourier lens.

Download Full Size | PPT Slide | PDF

Another problem leading to a wrong assignment of the wavenumber axis in the spectrum is the varying linear sampling frequency νs of the interferogram. According to Eq. (7), it depends both on the distance of the virtual sources and on the focal length of the lens, leading to a shift of the wavenumber axis ν˜shift, according to Eq. (8). The wavenumber shift for the spectrometer configuration described above is depicted in Fig. 4(b):

νs(λ,T)=fF(λ,T)sQ(λ,T)·ppix,
ν˜shift=ν˜(1νs(λ,T)νs,design).
Another disadvantage of using lenses as Fourier optics is the temperature dependency of their transmittance [17].

3. PROPOSED DESIGN

Due to the drawbacks of lenses as Fourier optics in static spectrometers described in the previous section, we propose a novel design of a broadband static Fourier transform spectrometer (bsFTS) using a single-mirror interferometer and a commercially available spherical mirror as Fourier optics. A schematic depiction of the setup can be found in Fig. 5.

 

Fig. 5. (a) Top view of the proposed bsFTS. (b) Side view of the proposed bsFTS.

Download Full Size | PPT Slide | PDF

In analogy to Fig. 1, Fig. 5(a) shows a top view of the assembly. The convex lens is now replaced by a spherical mirror, which, like the lens, is on-axis in this dimension. In this way, the contrast along the x axis or interferogram axis is not limited by a tilt of the spherical mirror. After being collimated by the spherical mirror, light is then directed upward and parallel to the z axis by a plane fold mirror and finally interferes on the detector array. The side view in Fig. 5(b) shows that the spherical mirror is tilted slightly upward around the x axis by an angle ϕ, which should ideally be kept as small as possible to achieve a sufficient contrast along the y axis or averaging axis and therefore a high SNR without time averaging. The fold mirror is eventually tilted by an angle of α=90°ϕ around the optical axis so that the detector array can be placed in parallel to the xy plane.

In theory, this configuration eliminates many of the previously mentioned disadvantages of the Fourier lens setup. First, the focal plane of the spherical mirror is constant over a wide temperature range; second, it is completely independent of the wavenumber. Therefore, ideally there is no loss of Michelson contrast. In addition, the bandwidth of the system is no longer limited by the transmittivity of the lens but only by the characteristics of the beam splitter and the used detector. Figure 6(a) shows the wavenumber shift of this system. The only effect to consider here is the varying distance between the virtual sources sQ(λ,T), according to Eq. (4). The resulting wavenumber shift is small compared with Fig. 4(b) and can be corrected algorithmically without problems. In addition, when using a ZnSe beam splitter, there is no noticeable temperature dependence.

 

Fig. 6. (a) Simulation of the wavenumber shift due to a changing distance between the virtual sources and a fixed focal length of the spherical mirror. (b) Simulation of the standard deviation of optical path differences imaged onto the 2D detector by a tilted spherical mirror. The off-axis angle is 16° to the y axis.

Download Full Size | PPT Slide | PDF

In practice, problems may arise due to expansion of the components and temperature-dependent distances between them. This should be manageable by a proper mechanical design and will be investigated in future work. One of the main problems of using a tilted concave mirror, however, lies in the aberrations that have not been considered up to now. When using an off-axis spherical mirror as in this setup, imaging quality in the tilting direction deteriorates. This leads to an increasingly imprecise allocation of optical path differences on the 2D detector and thus to a loss of contrast in this direction. This effect increases with increasing the off-axis angle ϕ. Figure 6(b) shows the results of a ray-tracing simulation of the proposed setup with an off-axis angle of 16°. The OPD standard deviation increases along the averaging axis with an optimum at around one-third of the detector height and is relatively constant along the interferogram axis. As a result, in practice it may not be possible to average over the entire y dimension of the detector, but a certain region has to be selected. As in the experimental setup presented in Section 4, the detector dimensions amount to 13.6mm×10.2mm, and the focal length of the spherical mirror is set to 75 mm. The light source radius is again set to 1 mm, which approximately corresponds to the dimension of the real light source used in the experimental setup. While a spherical mirror is inexpensive and still provides sufficient results in this configuration, as can be seen from the measurement results in Section 5, it may still be interesting for the future to replace it with an optimized free-form mirror to compensate for the aberrations described above. In particular, a mirror comprising spherical and parabolic components might prove beneficial.

4. EXPERIMENTAL SETUP

Based on the theoretical considerations in Section 3, we set up a prototype of the bsFTS for transmission measurements using a spherical mirror as a Fourier element. A ray-tracing model of the assembly is shown in Fig. 7. A light source is collimated by an off-axis parabolic mirror OAP1 with a focal length of 50.8 mm and an off-axis angle of 45°. After passing a long-pass filter and the sample, light is focused again by OAP2, having a focal length of 101.6 mm and an off-axis angle of 90°. OAP2 is positioned in such a way that, contrary to Figs. 1 and 5, the focal point and thus the extended light source are created behind the beam splitter and exactly below the lowest point of the fold mirror. In this way, we are able to place the fold mirror close above the optical axis and thus keep the off-axis angle of the spherical mirror relatively small at 16°. The beam splitter is made of zinc selenide with a thickness of 3.1 mm and a diameter of 25 mm at a parallelism of less than 10 arc seconds. The plane mirror has a diameter of 12.7 mm.

 

Fig. 7. Ray-tracing model of the experimental transmission measurement setup.

Download Full Size | PPT Slide | PDF

After hitting the spherical concave mirror with a focal length of 75 mm and a diameter of 25 mm, light is eventually guided to the detector array by an additional fold mirror with a diameter of 20 mm. All mirrors are coated with protected gold. For the detector, we use the microbolometer array UV840A by GUIDE Infrared with 800pix×600pix and a customized broadband transparent germanium window. The pixel pitch amounts to 17 μm; therefore, the detection area is 13.6mm×10.2mm. In combination with a long-pass filter having a cut-in wavenumber of about 2770cm1, the pixel pitch of the camera and the distance of the virtual sources of about 6.6 mm, the selected focal length of the spherical mirror satisfies the Nyquist criterion, according to Eq. (3). In principle, it would also be possible to set up the prototype without a fold mirror by using a beam splitter with a smaller diameter and then placing the detector array perpendicular to the optical axis and directly above the beam splitter. However, adjusting and setting up the system with a fold mirror is somewhat easier because the detector array can simply be placed in parallel to the xy plane.

Figure 8 shows the corresponding laboratory prototype used to perform the experiments in the course of this paper. Most mounts were fabricated using a 3D printer, with Thorlabs components used for adjustment. For a light source, we use a broadband silicon carbide thermal emitter (Hawkeye Technologies IR-Si207); further, the off-axis parabolic mirrors and the spherical mirror can be adjusted with appropriate mounts (Thorlabs K6XS, Thorlabs POLARIS-K1 and Thorlabs KMSS/M), while the long-pass filter, beam splitter, and fold mirror are fixed. The decisive component for calibration is the plane mirror, which can be tilted by a Thorlabs KM05FL/M mount to ensure that the two central beams are aligned parallel to each other, as well as moved with a LINOS translation stage to allow the distance dbspm to be varied. It should be noted that the height of the setup is only adapted to other laboratory components and could easily be reduced.

 

Fig. 8. Photo of the current laboratory prototype used to carry out the experiments in this paper.

Download Full Size | PPT Slide | PDF

While this design is sufficient to verify the principle and test the system for bandwidth, spectral resolution, and signal-to-noise ratio in the course of this paper, the setup will be modified for future investigations. For example, the 3D printed parts should be replaced by materials with a low coefficient of thermal expansion to allow a verification of the long-term and temperature stability of the spectrometer.

5. MEASUREMENT RESULTS

For validation of the concept presented here, we use the above described transmission measurement setup to record background and transmission spectra. To verify the wavenumber accuracy of the setup, we measure a 3 ml polystyrene calibration foil with the broadband static Fourier spectrometer as well as with a classical laboratory FTIR instrument as a reference. First, we record the background spectrum of the system. The corresponding 2D detector image is shown in Fig. 9(a). In order to see the interference pattern more clearly, the image was high-pass filtered and zoomed to the midpeak area.

 

Fig. 9. (a) High-pass-filtered detector image of the background interference pattern recorded with the presented setup. Zoomed to the interferogram midpeak. (b) High-pass-filtered apodized 1D background interferogram averaged over the highlighted 350 pixels in the y direction. The signal is normalized to the maximum peak.

Download Full Size | PPT Slide | PDF

As expected from the simulation of the OPD standard deviation in Fig. 6(b), an area of about 350 pixels as highlighted can be identified where the contrast of the interferogram is quite high. Outside this region, the contrast decreases in both directions. This means that the achievable SNR is strongly dependent on the area of the detector image being evaluated. If an area too small or too large around the highest contrast is evaluated, either too few detector rows are available for averaging, or many detector rows with low contrast are considered, both resulting in low SNR values. The former can be compensated by averaging over time, leading to a trade-off between SNR and measurement speed. Therefore, as mentioned earlier, it could be interesting to replace the spherical mirror with a customized mirror to further improve the system performance.

For obtaining the 1D interferogram, as shown in Fig. 9(b), the detector image is averaged along the lines of equal optical path difference in the highlighted detector area, and a triangular window is applied for apodization. The signal is normalized to the maximum peak. It is apparent that the midpeak was shifted to one side of the detector array by adjusting the distance dbspm between the beam splitter and plane mirror accordingly. This leads to a greater maximum OPD in the interferogram and thus to a higher spectral resolution, according to Eq. (2). Here, OPDmax amounts to about 0.9 mm, which corresponds to a spectral resolution of about 12cm1.

In analogy, Fig. 10 shows the detector image and the averaged interferogram of the polystyrene sample. For allowing a better comparison with the background measurement, the signal in Fig. 10(b) is again normalized to the maximum peak of the background interferogram. As expected, the midpeak of the sample interferogram is clearly attenuated and the envelope of the signal is slightly broadened because the polystyrene absorbs a significant part of the incoming radiation.

 

Fig. 10. (a) High-pass-filtered detector image of the polystyrene interference pattern recorded with the presented setup. Zoomed to the interferogram midpeak. (b) High-pass-filtered apodized 1D polystyrene interferogram averaged over the highlighted 350 pixels in the y direction. The signal is normalized to the maximum peak of the background interferogram.

Download Full Size | PPT Slide | PDF

As described in great detail in [10], the interferogram is sampled nonlinearly in a single-mirror interferometer. Therefore, we use a nonuniform Fourier transform to obtain the spectra. The resulting background spectrum is shown in Fig. 11(a). Its shape is mainly determined by three influence factors. The upper end of the wavenumber range is defined by the transmittivity of the long-pass filter, as shown in Fig. 11(a). This filter cuts in at 2780cm1 and also causes the signal drops around 1225cm1 and 900cm1 due to poor transmission properties. The significant signal drop between 2375cm1 and 1800cm1 is caused by the microbolometer transfer function. This is determined, on the one hand, by the typical behavior of a 2.5 μm optical cavity [18] and, on the other hand, by the integrated germanium window. At the lower end of the wavenumber range, all three components show poor transmittance. The main factor here is the beam splitter, which is not coated for wavenumbers below 650cm1. Apparently, the performance of the spectrometer could be significantly improved by using customized parts for this specific spectral range. Furthermore, characteristic absorption peaks caused by CO2 and H2O molecules can be observed in the spectrum. Figure 11(b) contains the single-shot background signal-to-noise ratio of the broadband sFTS. Therefore, we record 500 consecutive background spectra and calculate the noise as the standard deviation of the signal. The SNR curve roughly follows the spectral intensity curve discussed above with maxima around 1350cm1 and 2560cm1.

 

Fig. 11. (a) Measured background spectrum using the presented prototype as well as transmittance curves of the long-pass filter, beam splitter, and microbolometer array influencing the background envelope. (b) Background signal-to-noise ratio of the proposed prototype averaging over 350 pixels in the y direction without time averaging.

Download Full Size | PPT Slide | PDF

Finally, as a verification of the wavenumber accuracy of the bsFTS, we calculate the transmission spectrum of the 3 ml polystyrene calibration foil and compare it with a classical FTIR laboratory device (Thermo Fisher—Avatar 300). The corresponding spectra are shown in Fig. 12. Here, the bsFTS spectrum was wavenumber-corrected with the results from Fig. 6(a). It can be clearly seen that the positions of the characteristic spectral bands of the calibration foil are correctly allocated by the bsFTS. Because the laboratory device is set to a higher spectral resolution of 8cm1, the absorption peaks of the bsFTS appear less pronounced. The slight offset of the transmittance in the area from 2100cm1 to 2800cm1 can be caused by different angles of penetration in the two measurement systems. The probe is placed in the focal point in the reference FTIR, whereas it is passed collimated in the bsFTS.

 

Fig. 12. Comparison of the proposed broadband static Fourier transform spectrometer (bsFTS) with a scanning FTIR by measuring a 3 mil polystyrene calibration standard.

Download Full Size | PPT Slide | PDF

6. SUMMARY AND OUTLOOK

In this paper, we presented a novel broadband static Fourier transform spectrometer for the mid-infrared spectral range using a spherical concave mirror as Fourier element. The design is based on a single-mirror interferometer and therefore works independently of the light source size, allowing high light throughput and high signal-to-noise ratios. Because no lenses are implied in this spectrometer, it can be used over a wide spectral range and, with a suitable mechanical design, in principle shows no temperature or wavelength dependence. As only optical standard components and an uncooled microbolometer array are employed, the spectrometer can be designed at a reasonable cost. After giving an overview of the basic principle of static single-mirror Fourier transform spectrometers and the source-doubling principle in general, we carried out simulations to investigate the system behavior with different Fourier optics. Whereas a lens suffers from a varying refractive index and therefore causes different contrasts and sampling frequencies in the interferogram, a spherical mirror is comparably stable. Also, we investigated the effects of a tilted mirror, which cause a loss of contrast in the tilt direction. Based on these considerations, we devise an experimental setup using a spherical mirror tilted around the averaging axis, therefore maintaining the contrast along the interferogram axis. The setup was evaluated in a spectral range from 2800cm1 to 600cm1 at a spectral resolution of 12cm1. Measurements showed a high single-shot SNR as well as sufficient wavenumber accuracy compared with a laboratory FTIR spectrometer. Future work will include setting up and evaluating a temperature-stable prototype, using customized optical elements to improve the spectrometer efficiency as well as increase the spectral resolution. One possible future application of the system is the use for environmental gas sensing in combination with a scanning FTIR spectrometer, as described in [19].

Funding

Bundesministerium für Wirtschaft und Energie (BMWi) (ZF4304602RR6).

Acknowledgment

We appreciate the funding by BMWi of Germany and the contributions from our project partner Comline Elektronik Elektrotechnik GmbH.

REFERENCES

1. P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley, 2007).

2. M.-L. Junttila, “Performance limits of stationary Fourier spectrometers,” J. Opt. Soc. Am. A. 8, 1457–1462 (1991). [CrossRef]  

3. M. J. Padgett and A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 519–528 (1995). [CrossRef]  

4. F. M. Reininger, “The application of large format, broadband quantum well infrared photodetector arrays to spatially modulated prism interferometers,” Infrared Phys. Technol. 42, 345–362(2001). [CrossRef]  

5. J. V. Sweedler and M. B. Denton, “Spatially encoded Fourier transform spectroscopy in the ultraviolet to near-infrared,” Appl. Spectrosc. 43, 1378–1384 (1989). [CrossRef]  

6. T. Okamoto, S. Kawata, and S. Minami, “Fourier transform spectrometer with a self-scanning photodiode array,” Appl. Opt. 23, 269–273 (1984). [CrossRef]  

7. G. Zhan, “Static Fourier-transform spectrometer with spherical reflectors,” Appl. Opt. 41, 560–563 (2002). [CrossRef]  

8. H. Mortimer, “Compact interferometer spectrometer,” U.S. patent 9,046,412 (2 June 2015).

9. P. G. Lucey, K. Horton, T. Williams, K. Hinck, and C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–142 (1993). [CrossRef]  

10. M. Schardt, P. J. Murr, M. S. Rauscher, A. J. Tremmel, B. R. Wiesent, and A. W. Koch, “Static Fourier transform infrared spectrometer,” Opt. Express 24, 7767–7776 (2016). [CrossRef]  

11. M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Gas measurement using static Fourier transform infrared spectrometers,” Sensors 17, 2612 (2017). [CrossRef]  

12. M. Schardt, A. J. Tremmel, M. S. Rauscher, P. J. Murr, and A. W. Koch, “Spectral bandwidth limitations of static common-path and single-mirror Fourier transform infrared spectrometers,” Proc. SPIE 10210, 102100X (2017).

13. M. Schardt, C. Schwaller, A. J. Tremmel, and A. W. Koch, “Thermal stabilization of static single-mirror Fourier transform spectrometers,” Proc. SPIE 10210, 102100X (2017). [CrossRef]  

14. M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Measurement rates of static single-mirror Fourier transform infrared spectrometers using microbolometer detectors,” Tech. Mess. 84, 144–156 (2017).

15. L. Greengard and J.-Y. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev. 46, 443–454 (2004). [CrossRef]  

16. N. P. Barnes and M. S. Piltch, “Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium,” J. Opt. Soc. Am. 69, 178–180 (1979). [CrossRef]  

17. D. T. Gillespie, A. L. Olsen, and L. W. Nichols, “Transmittance of optical materials at high temperatures in the 1-m to 12-m range,” Appl. Opt. 4, 1488–1493 (1965). [CrossRef]  

18. J. L. Tissot, C. Trouilleau, B. Fieque, A. Crastes, and O. Legras, “Uncooled microbolometer detector: recent development at ULIS,” Opto-Electronics Rev. 14, 25–32 (2006). [CrossRef]  

19. J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley, 2007).
  2. M.-L. Junttila, “Performance limits of stationary Fourier spectrometers,” J. Opt. Soc. Am. A. 8, 1457–1462 (1991).
    [Crossref]
  3. M. J. Padgett and A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 519–528 (1995).
    [Crossref]
  4. F. M. Reininger, “The application of large format, broadband quantum well infrared photodetector arrays to spatially modulated prism interferometers,” Infrared Phys. Technol. 42, 345–362(2001).
    [Crossref]
  5. J. V. Sweedler and M. B. Denton, “Spatially encoded Fourier transform spectroscopy in the ultraviolet to near-infrared,” Appl. Spectrosc. 43, 1378–1384 (1989).
    [Crossref]
  6. T. Okamoto, S. Kawata, and S. Minami, “Fourier transform spectrometer with a self-scanning photodiode array,” Appl. Opt. 23, 269–273 (1984).
    [Crossref]
  7. G. Zhan, “Static Fourier-transform spectrometer with spherical reflectors,” Appl. Opt. 41, 560–563 (2002).
    [Crossref]
  8. H. Mortimer, “Compact interferometer spectrometer,” U.S. patent9,046,412 (2June2015).
  9. P. G. Lucey, K. Horton, T. Williams, K. Hinck, and C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–142 (1993).
    [Crossref]
  10. M. Schardt, P. J. Murr, M. S. Rauscher, A. J. Tremmel, B. R. Wiesent, and A. W. Koch, “Static Fourier transform infrared spectrometer,” Opt. Express 24, 7767–7776 (2016).
    [Crossref]
  11. M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Gas measurement using static Fourier transform infrared spectrometers,” Sensors 17, 2612 (2017).
    [Crossref]
  12. M. Schardt, A. J. Tremmel, M. S. Rauscher, P. J. Murr, and A. W. Koch, “Spectral bandwidth limitations of static common-path and single-mirror Fourier transform infrared spectrometers,” Proc. SPIE 10210, 102100X (2017).
  13. M. Schardt, C. Schwaller, A. J. Tremmel, and A. W. Koch, “Thermal stabilization of static single-mirror Fourier transform spectrometers,” Proc. SPIE 10210, 102100X (2017).
    [Crossref]
  14. M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Measurement rates of static single-mirror Fourier transform infrared spectrometers using microbolometer detectors,” Tech. Mess. 84, 144–156 (2017).
  15. L. Greengard and J.-Y. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev. 46, 443–454 (2004).
    [Crossref]
  16. N. P. Barnes and M. S. Piltch, “Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium,” J. Opt. Soc. Am. 69, 178–180 (1979).
    [Crossref]
  17. D. T. Gillespie, A. L. Olsen, and L. W. Nichols, “Transmittance of optical materials at high temperatures in the 1-m to 12-m range,” Appl. Opt. 4, 1488–1493 (1965).
    [Crossref]
  18. J. L. Tissot, C. Trouilleau, B. Fieque, A. Crastes, and O. Legras, “Uncooled microbolometer detector: recent development at ULIS,” Opto-Electronics Rev. 14, 25–32 (2006).
    [Crossref]
  19. J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
    [Crossref]

2017 (4)

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Gas measurement using static Fourier transform infrared spectrometers,” Sensors 17, 2612 (2017).
[Crossref]

M. Schardt, A. J. Tremmel, M. S. Rauscher, P. J. Murr, and A. W. Koch, “Spectral bandwidth limitations of static common-path and single-mirror Fourier transform infrared spectrometers,” Proc. SPIE 10210, 102100X (2017).

M. Schardt, C. Schwaller, A. J. Tremmel, and A. W. Koch, “Thermal stabilization of static single-mirror Fourier transform spectrometers,” Proc. SPIE 10210, 102100X (2017).
[Crossref]

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Measurement rates of static single-mirror Fourier transform infrared spectrometers using microbolometer detectors,” Tech. Mess. 84, 144–156 (2017).

2016 (2)

M. Schardt, P. J. Murr, M. S. Rauscher, A. J. Tremmel, B. R. Wiesent, and A. W. Koch, “Static Fourier transform infrared spectrometer,” Opt. Express 24, 7767–7776 (2016).
[Crossref]

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

2006 (1)

J. L. Tissot, C. Trouilleau, B. Fieque, A. Crastes, and O. Legras, “Uncooled microbolometer detector: recent development at ULIS,” Opto-Electronics Rev. 14, 25–32 (2006).
[Crossref]

2004 (1)

L. Greengard and J.-Y. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev. 46, 443–454 (2004).
[Crossref]

2002 (1)

2001 (1)

F. M. Reininger, “The application of large format, broadband quantum well infrared photodetector arrays to spatially modulated prism interferometers,” Infrared Phys. Technol. 42, 345–362(2001).
[Crossref]

1995 (1)

M. J. Padgett and A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 519–528 (1995).
[Crossref]

1993 (1)

P. G. Lucey, K. Horton, T. Williams, K. Hinck, and C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–142 (1993).
[Crossref]

1991 (1)

M.-L. Junttila, “Performance limits of stationary Fourier spectrometers,” J. Opt. Soc. Am. A. 8, 1457–1462 (1991).
[Crossref]

1989 (1)

1984 (1)

1979 (1)

1965 (1)

Barnes, N. P.

Budney, C.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, and C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–142 (1993).
[Crossref]

Chen, J.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Crastes, A.

J. L. Tissot, C. Trouilleau, B. Fieque, A. Crastes, and O. Legras, “Uncooled microbolometer detector: recent development at ULIS,” Opto-Electronics Rev. 14, 25–32 (2006).
[Crossref]

de Haseth, J. A.

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley, 2007).

Denton, M. B.

Dubey, M. K.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Fieque, B.

J. L. Tissot, C. Trouilleau, B. Fieque, A. Crastes, and O. Legras, “Uncooled microbolometer detector: recent development at ULIS,” Opto-Electronics Rev. 14, 25–32 (2006).
[Crossref]

Franklin, J. E.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Gillespie, D. T.

Gottlieb, E. W.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Greengard, L.

L. Greengard and J.-Y. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev. 46, 443–454 (2004).
[Crossref]

Griffiths, P. R.

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley, 2007).

Harvey, A. R.

M. J. Padgett and A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 519–528 (1995).
[Crossref]

Hedelius, J. K.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Hinck, K.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, and C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–142 (1993).
[Crossref]

Horton, K.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, and C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–142 (1993).
[Crossref]

Jones, T.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Junttila, M.-L.

M.-L. Junttila, “Performance limits of stationary Fourier spectrometers,” J. Opt. Soc. Am. A. 8, 1457–1462 (1991).
[Crossref]

Kawata, S.

Koch, A. W.

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Gas measurement using static Fourier transform infrared spectrometers,” Sensors 17, 2612 (2017).
[Crossref]

M. Schardt, A. J. Tremmel, M. S. Rauscher, P. J. Murr, and A. W. Koch, “Spectral bandwidth limitations of static common-path and single-mirror Fourier transform infrared spectrometers,” Proc. SPIE 10210, 102100X (2017).

M. Schardt, C. Schwaller, A. J. Tremmel, and A. W. Koch, “Thermal stabilization of static single-mirror Fourier transform spectrometers,” Proc. SPIE 10210, 102100X (2017).
[Crossref]

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Measurement rates of static single-mirror Fourier transform infrared spectrometers using microbolometer detectors,” Tech. Mess. 84, 144–156 (2017).

M. Schardt, P. J. Murr, M. S. Rauscher, A. J. Tremmel, B. R. Wiesent, and A. W. Koch, “Static Fourier transform infrared spectrometer,” Opt. Express 24, 7767–7776 (2016).
[Crossref]

Köhler, M. H.

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Gas measurement using static Fourier transform infrared spectrometers,” Sensors 17, 2612 (2017).
[Crossref]

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Measurement rates of static single-mirror Fourier transform infrared spectrometers using microbolometer detectors,” Tech. Mess. 84, 144–156 (2017).

Lee, J.-Y.

L. Greengard and J.-Y. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev. 46, 443–454 (2004).
[Crossref]

Legras, O.

J. L. Tissot, C. Trouilleau, B. Fieque, A. Crastes, and O. Legras, “Uncooled microbolometer detector: recent development at ULIS,” Opto-Electronics Rev. 14, 25–32 (2006).
[Crossref]

Lucey, P. G.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, and C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–142 (1993).
[Crossref]

Minami, S.

Mortimer, H.

H. Mortimer, “Compact interferometer spectrometer,” U.S. patent9,046,412 (2June2015).

Murr, P. J.

M. Schardt, A. J. Tremmel, M. S. Rauscher, P. J. Murr, and A. W. Koch, “Spectral bandwidth limitations of static common-path and single-mirror Fourier transform infrared spectrometers,” Proc. SPIE 10210, 102100X (2017).

M. Schardt, P. J. Murr, M. S. Rauscher, A. J. Tremmel, B. R. Wiesent, and A. W. Koch, “Static Fourier transform infrared spectrometer,” Opt. Express 24, 7767–7776 (2016).
[Crossref]

Nichols, L. W.

Okamoto, T.

Olsen, A. L.

Padgett, M. J.

M. J. Padgett and A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 519–528 (1995).
[Crossref]

Parker, H.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Piltch, M. S.

Rauscher, M. S.

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Measurement rates of static single-mirror Fourier transform infrared spectrometers using microbolometer detectors,” Tech. Mess. 84, 144–156 (2017).

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Gas measurement using static Fourier transform infrared spectrometers,” Sensors 17, 2612 (2017).
[Crossref]

M. Schardt, A. J. Tremmel, M. S. Rauscher, P. J. Murr, and A. W. Koch, “Spectral bandwidth limitations of static common-path and single-mirror Fourier transform infrared spectrometers,” Proc. SPIE 10210, 102100X (2017).

M. Schardt, P. J. Murr, M. S. Rauscher, A. J. Tremmel, B. R. Wiesent, and A. W. Koch, “Static Fourier transform infrared spectrometer,” Opt. Express 24, 7767–7776 (2016).
[Crossref]

Reininger, F. M.

F. M. Reininger, “The application of large format, broadband quantum well infrared photodetector arrays to spatially modulated prism interferometers,” Infrared Phys. Technol. 42, 345–362(2001).
[Crossref]

Schardt, M.

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Gas measurement using static Fourier transform infrared spectrometers,” Sensors 17, 2612 (2017).
[Crossref]

M. Schardt, A. J. Tremmel, M. S. Rauscher, P. J. Murr, and A. W. Koch, “Spectral bandwidth limitations of static common-path and single-mirror Fourier transform infrared spectrometers,” Proc. SPIE 10210, 102100X (2017).

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Measurement rates of static single-mirror Fourier transform infrared spectrometers using microbolometer detectors,” Tech. Mess. 84, 144–156 (2017).

M. Schardt, C. Schwaller, A. J. Tremmel, and A. W. Koch, “Thermal stabilization of static single-mirror Fourier transform spectrometers,” Proc. SPIE 10210, 102100X (2017).
[Crossref]

M. Schardt, P. J. Murr, M. S. Rauscher, A. J. Tremmel, B. R. Wiesent, and A. W. Koch, “Static Fourier transform infrared spectrometer,” Opt. Express 24, 7767–7776 (2016).
[Crossref]

Schwaller, C.

M. Schardt, C. Schwaller, A. J. Tremmel, and A. W. Koch, “Thermal stabilization of static single-mirror Fourier transform spectrometers,” Proc. SPIE 10210, 102100X (2017).
[Crossref]

Sweedler, J. V.

Tissot, J. L.

J. L. Tissot, C. Trouilleau, B. Fieque, A. Crastes, and O. Legras, “Uncooled microbolometer detector: recent development at ULIS,” Opto-Electronics Rev. 14, 25–32 (2006).
[Crossref]

Tremmel, A. J.

M. Schardt, C. Schwaller, A. J. Tremmel, and A. W. Koch, “Thermal stabilization of static single-mirror Fourier transform spectrometers,” Proc. SPIE 10210, 102100X (2017).
[Crossref]

M. Schardt, A. J. Tremmel, M. S. Rauscher, P. J. Murr, and A. W. Koch, “Spectral bandwidth limitations of static common-path and single-mirror Fourier transform infrared spectrometers,” Proc. SPIE 10210, 102100X (2017).

M. Schardt, P. J. Murr, M. S. Rauscher, A. J. Tremmel, B. R. Wiesent, and A. W. Koch, “Static Fourier transform infrared spectrometer,” Opt. Express 24, 7767–7776 (2016).
[Crossref]

Trouilleau, C.

J. L. Tissot, C. Trouilleau, B. Fieque, A. Crastes, and O. Legras, “Uncooled microbolometer detector: recent development at ULIS,” Opto-Electronics Rev. 14, 25–32 (2006).
[Crossref]

Viatte, C.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Wennberg, P. O.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Wiesent, B. R.

Williams, T.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, and C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–142 (1993).
[Crossref]

Wofsy, S. C.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Zhan, G.

Appl. Opt. (3)

Appl. Spectrosc. (1)

Atmos. Chem. Phys. (1)

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Infrared Phys. Technol. (1)

F. M. Reininger, “The application of large format, broadband quantum well infrared photodetector arrays to spatially modulated prism interferometers,” Infrared Phys. Technol. 42, 345–362(2001).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A. (1)

M.-L. Junttila, “Performance limits of stationary Fourier spectrometers,” J. Opt. Soc. Am. A. 8, 1457–1462 (1991).
[Crossref]

Opt. Express (1)

Opto-Electronics Rev. (1)

J. L. Tissot, C. Trouilleau, B. Fieque, A. Crastes, and O. Legras, “Uncooled microbolometer detector: recent development at ULIS,” Opto-Electronics Rev. 14, 25–32 (2006).
[Crossref]

Proc. SPIE (3)

M. Schardt, A. J. Tremmel, M. S. Rauscher, P. J. Murr, and A. W. Koch, “Spectral bandwidth limitations of static common-path and single-mirror Fourier transform infrared spectrometers,” Proc. SPIE 10210, 102100X (2017).

M. Schardt, C. Schwaller, A. J. Tremmel, and A. W. Koch, “Thermal stabilization of static single-mirror Fourier transform spectrometers,” Proc. SPIE 10210, 102100X (2017).
[Crossref]

P. G. Lucey, K. Horton, T. Williams, K. Hinck, and C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–142 (1993).
[Crossref]

Rev. Sci. Instrum. (1)

M. J. Padgett and A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 519–528 (1995).
[Crossref]

Sensors (1)

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Gas measurement using static Fourier transform infrared spectrometers,” Sensors 17, 2612 (2017).
[Crossref]

SIAM Rev. (1)

L. Greengard and J.-Y. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev. 46, 443–454 (2004).
[Crossref]

Tech. Mess. (1)

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Measurement rates of static single-mirror Fourier transform infrared spectrometers using microbolometer detectors,” Tech. Mess. 84, 144–156 (2017).

Other (2)

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley, 2007).

H. Mortimer, “Compact interferometer spectrometer,” U.S. patent9,046,412 (2June2015).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1.
Fig. 1. Design principle of a static single-mirror Fourier transform spectrometer [10].
Fig. 2.
Fig. 2. Typical pattern of optical path differences generated by a single-mirror interferometer. The main path difference modulation occurs along the x axis. As indicated, the signal can be averaged along the curved lines of equal optical path difference along the y axis.
Fig. 3.
Fig. 3. Temperature- and wavelength-dependent virtual source model of a static single-mirror Fourier transform spectrometer.
Fig. 4.
Fig. 4. (a) Simulation of the Michelson contrast for typical lens-based spectrometer configurations. Solid lines indicate a focal length of 75 mm, dashed lines a focal length of 40 mm. The radius of the light source is set to 1 mm. (b) Simulation of the wavenumber shift due to a changing distance between the virtual sources and a varying focal length of the Fourier lens.
Fig. 5.
Fig. 5. (a) Top view of the proposed bsFTS. (b) Side view of the proposed bsFTS.
Fig. 6.
Fig. 6. (a) Simulation of the wavenumber shift due to a changing distance between the virtual sources and a fixed focal length of the spherical mirror. (b) Simulation of the standard deviation of optical path differences imaged onto the 2D detector by a tilted spherical mirror. The off-axis angle is 16° to the y axis.
Fig. 7.
Fig. 7. Ray-tracing model of the experimental transmission measurement setup.
Fig. 8.
Fig. 8. Photo of the current laboratory prototype used to carry out the experiments in this paper.
Fig. 9.
Fig. 9. (a) High-pass-filtered detector image of the background interference pattern recorded with the presented setup. Zoomed to the interferogram midpeak. (b) High-pass-filtered apodized 1D background interferogram averaged over the highlighted 350 pixels in the y direction. The signal is normalized to the maximum peak.
Fig. 10.
Fig. 10. (a) High-pass-filtered detector image of the polystyrene interference pattern recorded with the presented setup. Zoomed to the interferogram midpeak. (b) High-pass-filtered apodized 1D polystyrene interferogram averaged over the highlighted 350 pixels in the y direction. The signal is normalized to the maximum peak of the background interferogram.
Fig. 11.
Fig. 11. (a) Measured background spectrum using the presented prototype as well as transmittance curves of the long-pass filter, beam splitter, and microbolometer array influencing the background envelope. (b) Background signal-to-noise ratio of the proposed prototype averaging over 350 pixels in the y direction without time averaging.
Fig. 12.
Fig. 12. Comparison of the proposed broadband static Fourier transform spectrometer (bsFTS) with a scanning FTIR by measuring a 3 mil polystyrene calibration standard.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

I ( x , y ) = 0 S ( ν ˜ ) B ( ν ˜ ) { 1 + cos ( 2 π ν ˜ ( x s Q f F + Δ x nonlin ( x , y ) ) ) } d ν ˜ .
Δ ν ˜ = 1 OPD max 2 · ν ˜ max g m · N x .
ν ˜ max f F 2 · s Q · p pix .
s Q ( λ , T ) = d bs pm + T bs · ( n s · sin ( π 4 arcsin ( n s n b s ( λ , T ) · 2 ) ) 1 ( n s n b s ( λ , T ) · 2 ) 2 ) .
Δ f F ( λ , T ) = f F , des · n des n ( λ , T ) n ( λ , T ) 1 .
n ( λ , T ) = ( A + B λ 2 ( λ 2 C ) + D λ 2 ( λ 2 E ) ) 1 / 2 .
ν s ( λ , T ) = f F ( λ , T ) s Q ( λ , T ) · p pix ,
ν ˜ shift = ν ˜ ( 1 ν s ( λ , T ) ν s , design ) .

Metrics