Broadband high-spectral-resolution ultraviolet-visible coherent-dispersion imaging spectrometer

Qinghua Yang

doi:10.1364/OE.26.020777

1. Introduction

Imaging spectrometry combines imaging and spectroscopy to get both spatial and spectral information of an object or a scene. Although imaging spectrometry was originally designed for Earth remote sensing [1], it is currently much used for various kinds of scientific research and industrial applications [2,3]. According to different spectral information detection methods, imaging spectrometers are divided into three categories. The first category is color filter imaging spectrometer that uses either a set of band-pass filters, a circular-variable filter [4], a liquid-crystal tunable filter [5–8] or an acousto-optical tunable filter [9–14] to measure a spectral image. The second category is dispersive imaging spectrometer that uses a prism or a grating to achieve the dispersion of light and also employs either whisk-broom scanning [15], push-broom scanning [16], staring [17–22] or snapshot (i.e., snapshot spectral imagers) [23–25] to obtain a data cube. The third category is interferometric imaging spectrometer (i.e., Fourier transform imaging spectrometer) that is based on temporal interferometry or spatial interferometry [26–39].

The multiplex (Fellgett) [40,41] advantage of interferometric spectrometry over dispersive spectrometry is fully valid only when the detector noise exceeds all other noise sources and is independent of the power of the radiation incident on the detector, which is the usual case for the infrared spectrometry. On the contrary, in the ultraviolet-visible spectral region, the photon noise is the limiting factor, the noise level is proportional to the square root of the incident power, and also the multiplex gain depends on the square root of the ratio of the intensity of a spectral line to the mean intensity of the whole spectra [34]. The interferometric spectrometry performance is weakened for measuring a broadband source in the ultraviolet-visible spectral region [42]. More importantly, the multiplex disadvantage is one of the greatest disadvantages of existing ultraviolet-visible multiplexed spectrometers for a broadband source [42–47]. In addition to filtering the light before detection [48–52], the coherent-dispersion spectrometry reported in [53] is a very good solution to the above-mentioned multiplex disadvantage.

This paper reports a coherent-dispersion imaging spectrometer, which integrates a dynamic imaging interferometer and a dispersing prism. After a detailed description of the principle, the design calculations are illustrated by an example for the spectral range from 200 nm to 700 nm, the numerical simulations are shown for the interferogram and spectrum, and finally the conclusion is given.

2. Principle

Figure 1 shows the optical layout of a broadband high-spectral-resolution coherent-dispersion imaging spectrometer (CDIS), which integrates a moving corner-cube-mirror interferometer and a dispersing prism. The moving corner-cube-mirror interferometer consists of one moving corner-cube mirror (CCM), one fixed CCM, and one beam splitter. The entrance slit is located at the front focal plane of the collimating lens, and the two-dimensional detector is located at the back focal plane of the collecting lens. The entrance slit may coincide with a real emitting surface, or may be located at the back focal plane of a telescope or microscope. The light from each unit of the entrance slit is converted into a parallel beam by a collimating lens and then is divided into two beams by the beam splitter. One beam is reflected by the moving CCM, the other is reflected by the fixed CCM. After returning to and leaving the beam splitter, these two beams are dispersed by a dispersing prism in y-axis direction and then are collected by a collecting lens in both x-axis and y-axis directions; finally they are received by the detector to be transformed into a useful electrical signal. Since interferometry is used to directly discern temporal coherence properties of the incident light and a dispersing prism is used to disperse the incident light, the name of the proposed imaging spectrometer is called the coherent-dispersion imaging spectrometer (CDIS).

Fig. 1 Optical layout of the coherent-dispersion imaging spectrometer (CDIS) combining a moving corner-cube-mirror interferometer and a dispersing prism. ZPD: zero phase difference.

Download Full Size | PDF

The CDIS combines imaging, interferometric spectrometry and dispersive spectrometry to get both spatial and spectral information of an object or a scene with a wide spectral range in the ultraviolet-visible spectral region. On the one hand (imaging), the CDIS images each unit of the entrance slit on a separate column of the detector. More specifically, each unit of the entrance slit is imaged on a given column of a detector, and different wavelengths are dispersed across different rows of that column. On the other hand (spectroscopy), for each unit of the entrance slit, the CDIS produces multiple interferograms simultaneously in one scan period of the moving CCM, each interferogram covering a separate wavelength range controlled by the dispersing prism and detector geometry, each interferogram located in a separate pixel of the detector. More specifically, for each unit of the entrance slit, not only the dispersing prism spreads the spectral information onto a separate column of the detector, but also the interferometer generates multiple interferograms simultaneously in one scan period of the moving CCM, each interferogram with a separate wavelength range and located in a separate pixel of the detector. For the CDIS, any noise present in an optical signal is limited to the pixels where this noisy signal impinges on, and these noise signals have no effect on the interferograms with different wavelength ranges. The spectra from any narrowband interferogram are different, but the sum of the spectra from all narrowband interferograms constitutes a continuous spectrum of the source. The CDIS is a unique concept to greatly reduce the multiplex disadvantage of existing ultraviolet-visible multiplexed spectroscopy while achieving imaging combined with high spectral resolution for a wide spectral range. Due to the use of an entrance slit, the CDIS forms one-dimensional images. However, the CDIS can form two-dimensional images when it is spatially scanned transverse to the entrance slit. Namely, if the push-broom scanning is perpendicular to the entrance slit, the push-broom CDIS forms a two-dimensional image.

In Fig. 1, typical rays emerging from two representative points of the entrance slit are drawn. One point, A, is located on the optical axis of the collimating lens. The second point, B, is displaced by a distance $x^{'}$ from the optical axis. Moreover, four representative image points are shown. $A_{1}$ is the image point of object point A formed by narrow waveband 1, $A_{k}$ is the image point of object point A formed by narrow waveband k, both $A_{1}$ and $A_{k}$ are located in the column $i$ of the detector (the column $i$ intersects the optical axis of the collecting lens). $B_{1}$ is the image point of object point B formed by narrow waveband 1, $B_{k}$ is the image point of object point B formed by narrow waveband k, both $B_{1}$ and $B_{k}$ are located in the column $j$ of the detector. Both $A_{1}$ and $B_{1}$ are located in the row 1 of the detector, and the distance between $A_{1}$ and $B_{1}$ is $x$ . Both $A_{k}$ and $B_{k}$ are located in the row k of the detector, and the distance between $A_{k}$ and $B_{k}$ is $x$ . Throughout this paper, rows of the detector are parallel to the x-axis, and columns of the detector are parallel to the y-axis. $l$ is the displacement of the moving CCM from the zero phase difference (ZPD) position, $f_{1}$ is the focal length of the collimating lens, and $f_{2}$ is the focal length of the collecting lens.

Figure 2 shows the equivalent light path diagram in the sagittal plane of the CDIS. Let the x-axis coordinate of the image points (e.g. $A_{1}$ and $A_{k}$ ) of object point A at the detector plane be zero, so the x-axis coordinate of the image points (e.g. $B_{1}$ and $B_{k}$ ) of object point B at the detector plane is $x$ . The angle between the emergent rays of the interferometer and the optical axis of the collecting lens, i.e., the angle between the collimated rays and the optical axis of the collimating lens as shown in Fig. 2, is given by

Fig. 2 Equivalent light path diagram in the sagittal plane of the CDIS.

Download Full Size | PDF

\tan θ = \frac{x^{'}}{f_{1}} = \frac{x}{f_{2}} .

If the pixel size of the detector is $b$ , according to Eq. (1), the spatial resolution of the CDIS to the entrance slit is determined by

δ x^{'} = b \frac{f_{1}}{f_{2}},

and the angular resolution of the CDIS to the entrance slit is determined by

δ θ = arc \tan (\frac{b}{f_{2}}) .

If the length of the entrance slit is $2 {x^{'}}_{\max}$ , based on Eq. (1), the size of each row (in x-axis direction) of the detector must be greater than $2 {x^{'}}_{\max} f_{2} / f_{1}$ . Let $N$ denote the number of pixels in each row of the detector used to record the spectral image, and so

N > \frac{2 {x^{'}}_{\max}}{b} \frac{f_{2}}{f_{1}} .

The optical path difference, $Δ$ , for each interferogram generated by the light emerging from the object point B displaced by a distance $x^{'}$ from the optical axis is given by [28,35]

Δ (l, x) = \frac{2 l}{\cos θ} = 2 l \sqrt{1 + \tan^{2} θ} = 2 l \sqrt{1 + \frac{x^{2}}{f_{2}^{2}}} .

The interferogram $I (l, x)$ generated by the light emerging from the object point B displaced by a distance $x^{'}$ from the optical axis of the collimating lens is given by

I (l, x) = \int_{0}^{\infty} B (σ) [1 + \cos (4 π σ l \sqrt{1 + \frac{x^{2}}{f_{2}^{2}}})] d σ .

where

σ

is the wave number,

B (σ)

is the input spectral intensity at a wavenumber

σ

,

l

is the displacement of the moving CCM from the zero phase difference (ZPD) position, and

x

is the x-axis coordinate of the image points (e.g.

B_{1}

and

B_{k}

) of object point B at the detector plane. For the object point A that is located on the optical axis of the collimating lens,

x^{'} = 0

, so

θ = 0

,

x = 0

, the optical path difference simplifies to be

Δ = 2 l

, and Eq. (6) simplifies to be

I (Δ) = \int_{0}^{\infty} B (σ) [1 + \cos (2 π σ Δ)] d σ

.

From Eq. (5), the maximum optical path difference for each interferogram generated by the light emerging from the object point B is

Δ_{\max} (l, x) = \frac{2 l_{\max}}{\cos θ} = 2 l_{\max} \sqrt{1 + \frac{x^{2}}{f_{2}^{2}}} .

where

l_{\max}

is the maximum displacement of the moving CCM from the ZPD position.

The spectral resolution $δ σ$ for each interferogram is determined by

δ σ = \frac{1}{2 \cdot Δ_{\max}},

and therefore, the theoretical spectral resolution for each interferogram generated by the light emerging from the object point B is

δ σ = \frac{\cos θ}{4 l_{\max}} = \frac{1}{4 l_{\max} \sqrt{1 + \frac{x^{2}}{f_{2}^{2}}}} .

Since

x

is generally much smaller than

f_{2}

, the theoretical spectral resolution for each interferogram generated by the light emerging from the object point A located on the optical axis is generally used as the theoretical spectral resolution of the CDIS. Thus, in practical instrument design, the theoretical spectral resolution of the CDIS can be calculated by

δ σ = \frac{1}{4 l_{\max}} .

In practice, in order to improve the signal-to-noise ratio of the recovered spectrum, the truncation and apodization (e.g. the triangular function) of the interferogram will reduce the spectral resolution. Consequently, for the instrument design in engineering, the practical spectral resolution of the CDIS can be calculated by

δ σ^{'} = \frac{1}{2 l_{\max}} .

According to Nyquist criterion, for convenience, the sampling interval $L$ for each interferogram produced by the CDIS can be

L \leq \frac{1}{2 σ_{\max}} .

where

σ_{\max}

is the maximum wave number of the source spectrum.

The sampling interval $L$ for each interferogram generated by the light emerging from the object point B is given by

L \cdot K (x) = Δ_{\max} (l, x) = 2 l_{\max} \sqrt{1 + \frac{x^{2}}{f_{2}^{2}}} .

where

K (x)

is the number of sampling points for each unilateral interferogram generated by the light emerging from the object point B displaced by a distance

x^{'}

from the optical axis. Based on Eqs. (12) and (13), it can be obtained that

K (x) = 4 σ_{\max} l_{\max} \sqrt{1 + \frac{x^{2}}{f_{2}^{2}}} .

The number of sampling points for each unilateral interferogram generated by the light emerging from the object point A located on the optical axis is

K (0) = 4 σ_{\max} l_{\max}

. From Eqs. (9) and (14), the resolving power

R

for each interferogram generated by the light emerging from the object point B displaced by a distance

x^{'}

from the optical axis is determined by the number of sampling points for the interferogram, i.e.,

R = σ_{\max} / δ σ = K (x)

. For the spatial interferometry (e.g. the Sagnac interferometer), the resolving power is determined by the number of pixels per row of the detector [53]. It can be easily obtained that the number of sampling points for the interferogram can be much larger than the number of pixels per row of the detector. Therefore, the resolving power of the CDIS can be much higher than that of the spatial interferometry.

Figure 3 shows the equivalent light path diagram in the meridian plane of the CDIS. Suppose that $γ$ is the vertex angle of the dispersing prism with an isosceles triangle structure, $n (λ_{i})$ is the refractive index of the dispersing prism for wavelength $λ_{i}$ , $λ_{c}$ is the central wavelength of the source spectrum, $y (λ_{c})$ is the y-axis coordinate for central wavelength $λ_{c}$ at the detector plane, and $y (λ_{i})$ is the y-axis coordinate for wavelength $λ_{i}$ at the detector plane. A ray from the interferometer enters the dispersing prism at angle $α$ , is refracted at angle $θ_{1} (λ_{i})$ on the first surface, reaches the second surface at angle $θ_{2} (λ_{i})$ , and leaves the prism at angle $θ_{3} (λ_{i})$ . Let the optical axis of the collecting lens overlap with the light ray exiting the prism of the central wavelength $λ_{c}$ , therefore, the y-axis coordinate of central wavelength $λ_{c}$ at the detector plane is zero, i.e., $y (λ_{c}) = 0$ . According to the law of refraction, the characteristics of the lens and the geometry, it can be obtained that

Fig. 3 Equivalent light path diagram in the meridian plane of the CDIS.

Download Full Size | PDF

\sin α = n (λ_{i}) \sin θ_{1} (λ_{i}),

θ_{1} (λ_{i}) + θ_{2} (λ_{i}) = γ,

n (λ_{i}) \sin θ_{2} (λ_{i}) = \sin θ_{3} (λ_{i}),

β (λ_{i}) = θ_{3} (λ_{C}) - θ_{3} (λ_{i}),

y (λ_{i}) = f_{2} \cdot \tan β (λ_{i}) .

From Eqs. (15)-(19), the y-axis coordinate for wavelength $λ_{i}$ at the detector plane can be written as

y (λ_{i}) = f_{2} \cdot \frac{τ (λ_{C}) - τ (λ_{i})}{1 + τ (λ_{C}) \cdot τ (λ_{i})},

where

τ (λ) = \frac{\sin γ \sqrt{n^{2} (λ) - \sin^{2} α} - \cos γ \sin α}{\sqrt{1 - {(\sin γ \sqrt{n^{2} (λ) - \sin^{2} α} - \cos γ \sin α)}^{2}}} .

As a result, the interferogram k generated by the light emerging from any object point of the entrance slit is located in the row k of the detector and covers a wavelength range from

λ_{k 1}

to

λ_{k q}

(i.e., wavenumber range from

σ_{k q} = 1 / λ_{k q}

to

σ_{k 1} = 1 / λ_{k 1}

, because

λ_{k 1} < λ_{k q}

) which are determined by

| y (λ_{k q}) - y (λ_{k 1}) | \leq b .

If the source spectrum covers a wavelength range from $λ_{\min}$ to $λ_{\max}$ (i.e., a wavenumber range from $σ_{\min} = 1 / λ_{\max}$ to $σ_{\max} = 1 / λ_{\min}$ ), the size of each column (in y-axis direction) of the detector must be greater than $| y (λ_{\max}) - y (λ_{\min}) |$ . Let $M$ denote the number of pixels in each column of the detector used to acquire multiple interferograms. Therefore, for each object point of the entrance slit, $M$ separate interferograms are generated simultaneously in one scan period of the moving CCM. It can be obtained that

M \geq \frac{| y (λ_{\max}) - y (λ_{\min}) |}{b} .

Table 1 shows the main advantages of the CDIS compared with temporal interferometry based on linear motion (e.g. the original moving corner-cube-mirror interferometer), temporal interferometry based on rotational motion, spatial interferometry, traditional dispersive imaging spectrometer, and color filter imaging spectrometer, respectively.

Table 1. Comparisons of the CDIS, interferometry, dispersive, and color filter approaches

View Table | View all tables in this article

Due to the multiplex disadvantage inherent in ultraviolet-visible interferometry, even if the maximum optical path difference as shown in Eq. (7) is the same, the CDIS can achieve higher spectral resolution than the original moving corner-cube-mirror interferometer for measuring a broadband source in the ultraviolet-visible spectral region.

Both the Andor iDus CCD and Newton CCD spectroscopy detectors of Oxford Instruments are suitable for the coherent-dispersion imaging spectrometer. For example, the Andor iDus 420 Series 1024 x 255 pixel Spectroscopy CCD, the Andor Newton 920 Series 1024 x 255 pixel Spectroscopy CCD, the Andor Newton 940 Series 2048 x 512 pixel Spectroscopy CCD, and so on.

3. Design calculation and numerical simulation

Assume that the source spectrum covers a wavelength range from 200 nm to 700 nm, i.e., a wavenumber range from 14285.7 cm⁻¹ to 50000 cm⁻¹. The wavelength difference versus wavenumber difference for several wavelengths are shown in Table 2. According to Table 2, if the desired spectral resolution (in wavelength) of the CDIS is 0.01 nm at 220 nm together with 0.1 nm at 700 nm, the practical spectral resolution (in wavenumber) of the CDIS should be $δ σ^{'} = 2 {cm}^{- 1}$ . For instrument design in engineering, according to Eqs. (10) and (11), the theoretical spectral resolution (in wavenumber) of the CDIS should be $δ σ = 1 {cm}^{- 1}$ . Therefore, based on Eq. (10) or Eq. (11), the maximum displacement of the moving CCM from the ZPD position should be $l_{\max} = 1 / (4 δ σ) = 1 / (2 δ σ^{'}) = 2.5 mm$ .

Table 2. Wavelength difference versus Wavenumber difference for several wavelengths

View Table | View all tables in this article

Suppose that the focal length of the collecting lens is $f_{2} = 400 mm$ , the focal length of the collimating lens is $f_{1} = 400 mm$ , and the pixel size of the detector is $b = 0.02 mm$ . According to Eq. (2), the spatial resolution of the CDIS to the entrance slit is $δ x^{'} = 0.02 m m \times 400 m m / 400 m m = 0.02 m m$ . From Eq. (3), the angular resolution of the CDIS to the entrance slit is $δ θ = \arctan (0.02 m m / 400 m m) = 0.0029 °$ . If the length of the entrance slit is $2 {x^{'}}_{\max} = 10 m m$ , based on Eq. (4), the number of pixels in each row of the detector is $N > 10 m m \times 400 m m / (400 m m \times 0.02 m m) = 500$ .

Fused silica is a proper material for the dispersing prism in a CDIS for the spectral range from 200 nm to 700 nm. The formula for the refractive index of fused silica is given by [54]

n^{2} = 1 + \frac{0.6961663 λ^{2}}{λ^{2} - {0.0684043}^{2}} + \frac{0.4079426 λ^{2}}{λ^{2} - {0.1162414}^{2}} + \frac{0.8974794 λ^{2}}{λ^{2} - {9.896161}^{2}}

Let the vertex angle of the dispersing prism be $γ = 49 °$ , let the incident angle to the dispersing prism be $α = 24.5 °$ , and let the central wavelength be $λ_{c} = 280 n m$ . According to Eqs. (20), (21) and (24), the y-axis coordinate for wavelength $λ_{i}$ at the detector plane is shown in Fig. 4. The y-axis coordinate for wavelength 700 nm is $y (λ_{700}) \approx 1.2263 m m$ , and the y-axis coordinate for wavelength 200 nm is $y (λ_{200}) \approx - 1.4766 m m$ . From Eq. (23), the number of pixels in each column of the detector is $M \geq | y (λ_{700}) - y (λ_{200}) | / b = 2.7029 / 0.02 = 135.1$ . As a result, for each unit of the entrance slit, 136 separate interferograms are generated simultaneously in one scan period of the moving CCM.

Fig. 4 The y-axis coordinate for different wavelengths at the detector plane.

Download Full Size | PDF

Table 3 shows the wavelength (wavenumber) ranges for several separate interferograms. The interferogram 1 is located in the row 1 of the detector and contains wavelength 700 nm, the interferogram 7 located in row 7 contains wavelength 555 nm, the interferogram 35 located in row 35 contains wavelength 350 nm, the interferogram 62 located in row 62 contains wavelength 280 nm, and the interferogram 109 located in row 109 contains wavelength 220 nm.

Table 3. Wavelength/wavenumber ranges of several separate Interferograms

View Table | View all tables in this article

According to Eq. (14), the number of sampling points for each unilateral interferogram generated by the light emerging from the object point A located on the optical axis is $K (0) = 4 σ_{\max} l_{\max} = 4 \times 50000 c m^{- 1} \times 2.5 m m = 50000$ . For the object point A located on the optical axis, according to Eqs. (6), (20), (21) and (24) together with the relevant parameter values, several unilateral interferograms (i.e., interferograms 1, 7, 35, 62 and 109 as shown in Table 3) generated by the CDIS in one scan period of the moving CCM are shown in Fig. 5.

Fig. 5 Several interferograms obtained simultaneously by the CDIS in one scan period of the moving CCM for object point A when the theoretical spectral resolution is 1 cm⁻¹.

Download Full Size | PDF

Figure 6 shows the CDIS spectrum obtained from Fourier transform of the several unilateral interferograms in Fig. 5. Spectral peaks in the range of 220 nm to 700 nm (i.e., 14285.7 cm⁻¹ to 45454.5 cm⁻¹) are visible.

Fig. 6 CDIS spectrum obtained from Fourier transform of several interferograms in Fig. 5.

Download Full Size | PDF

Figure 7 shows the CDIS interferogram 1 containing only wavelength 699.6 nm, 699.7 nm, 699.8 nm, 699.9 nm, 700 nm and the spectrum obtained from Fourier transform of the interferogram 1 for object point A when the theoretical spectral resolution is 1 cm⁻¹. Five spectral peaks are clearly visible. That is, the spectra of wavelengths 699.6 nm, 699.7 nm, 699.8 nm, 699.9 nm and 700 nm are obtained. Consequently, it can be easily obtained that the spectral resolution of the CDIS is at least 0.1 nm at 700 nm when the theoretical spectral resolution of the CDIS is 1 cm⁻¹.

Fig. 7 CDIS interferogram 1 containing only wavelength 699.6 nm, 699.7 nm, 699.8 nm, 699.9 nm, 700 nm and the Spectrum obtained from Fourier transform of the interferogram 1 for object point A when the theoretical spectral resolution is 1 cm⁻¹.

Download Full Size | PDF

Figure 8 shows the CDIS interferogram 35 containing only wavelength 349.94 nm, 349.97 nm, 350 nm, 350.03 nm, 350.06 nm and the spectrum obtained from Fourier transform of the interferogram 35 for object point A when the theoretical spectral resolution is 1 cm⁻¹. Spectral peaks of the five wavelengths are clearly distinguished. So it can be readily obtained that the spectral resolution of the CDIS is at least 0.03 nm at 350 nm when the theoretical spectral resolution of the CDIS is 1 cm⁻¹.

Fig. 8 CDIS interferogram 35 containing only wavelength 349.94 nm, 349.97 nm, 350 nm, 350.03 nm, 350.06 nm and the Spectrum obtained from Fourier transform of the interferogram 35 for object point A when the theoretical spectral resolution is 1 cm⁻¹.

Download Full Size | PDF

Figure 9 shows the CDIS interferogram 109 containing only wavelength 219.98 nm, 219.99 nm, 220 nm, 220.01 nm, 220.02 nm and the spectrum obtained from Fourier transform of the interferogram 109 for object point A when the theoretical spectral resolution is 1 cm⁻¹. Therefore, the spectral resolution of the CDIS is at least 0.01 nm at 220 nm when the theoretical spectral resolution of the CDIS is 1 cm⁻¹.

Fig. 9 CDIS interferogram 109 containing only wavelength 219.98 nm, 219.99 nm, 220 nm, 220.01 nm, 220.02 nm and the Spectrum obtained from Fourier transform of the interferogram 109 for object point A when the theoretical spectral resolution is 1 cm⁻¹.

Download Full Size | PDF

4. Conclusion

A coherent-dispersion imaging spectrometer (CDIS) was investigated, which offers significant advantages compared with existing ultraviolet-visible imaging spectrometer configurations. The CDIS can form a two-dimensional image when it is spatially scanned (e.g. push-broom scanning) perpendicular to the entrance slit. The CDIS combines imaging, interferometric spectroscopy and dispersive spectroscopy to get both spatial and spectral information of an object or a scene with a wide spectral range. The first important advantage of the CDIS, compared with conventional interferometric imaging spectrometers, is that the CDIS greatly reduces the multiplex disadvantage inherent in interferometry for ultraviolet-visible spectroscopy. The second important advantage of the CDIS, compared with traditional dispersive imaging spectrometers or spatial interferometry, is high spectral resolution for a broadband spectral range in the ultraviolet-visible spectral region. For the above-mentioned example, when the theoretical spectral resolution of the CDIS is 1 cm⁻¹, the spectral resolution (in wavelength) of the CDIS is at least 0.01 nm at 220 nm together with 0.1 nm at 700 nm for the spectral range from 200 nm to 700 nm. The third advantage of the CDIS, compared with the spatial interferometry or temporal interferometry, is that the dynamic range requirement of the detector is reduced. There is also a tradeoff for the CDIS, which mainly includes two aspects. First, while the CDIS benefits from the high spectral resolution of interferometry, the presence of an entrance slit means the instrument does not benefit from the throughput advantage. Second, to form a two-dimensional spectral image, both one corner-cube mirror and the entrance slit must be scanned, which will necessitate long scan times. In summary, the CDIS is a unique concept to greatly reduce the multiplex disadvantage of existing ultraviolet-visible multiplexed spectroscopy while achieving imaging combined with high spectral resolution for a broadband spectral range in the ultraviolet-visible spectral region. Although this is a design, no instrument or prototype is actually built or tested, and the calculations represent only the first-order optical effects (i.e., none of the aberrations of actual optical systems are present), the CDIS will be suitable for high-spectral-resolution broadband spectral imaging in the ultraviolet-visible spectral region.

Funding

National Natural Science Foundation of China (NSFC) (61605151).

References

1. A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging Spectrometry for Earth Remote Sensing,” Science 228(4704), 1147–1153 (1985). [CrossRef] [PubMed]

2. A. F. H. Goetz, “Three decades of hyperspectral remote sensing of the Earth: a personal view,” Remote Sens. Environ. 113, S5–S16 (2009). [CrossRef]

3. Q. Li, X. He, Y. Wang, H. Liu, D. Xu, and F. Guo, “Review of spectral imaging technology in biomedical engineering: achievements and challenges,” J. Biomed. Opt. 18(10), 100901 (2013). [CrossRef] [PubMed]

4. C. L. Wyatt, “Infrared spectrometer: Liquid-helium-cooled rocketborne circular-variable filter,” Appl. Opt. 14(12), 3086–3091 (1975). [CrossRef] [PubMed]

5. H. R. Morris, C. C. Hoyt, and P. J. Treado, “Imaging spectrometers for fluorescence and Raman microscopy: acousto-optic and liquid crystal tunable filters,” Appl. Spectrosc. 48(7), 857–866 (1994). [CrossRef]

6. S. C. Gebhart, R. C. Thompson, and A. Mahadevan-Jansen, “Liquid-crystal tunable filter spectral imaging for brain tumor demarcation,” Appl. Opt. 46(10), 1896–1910 (2007). [CrossRef] [PubMed]

7. Z. Zheng, G. Yang, H. Li, and X. Liu, “Three-stage Fabry-Perot liquid crystal tunable filter with extended spectral range,” Opt. Express 19(3), 2158–2164 (2011). [CrossRef] [PubMed]

8. M. Abuleil and I. Abdulhalim, “Narrowband multispectral liquid crystal tunable filter,” Opt. Lett. 41(9), 1957–1960 (2016). [CrossRef] [PubMed]

9. D. A. Glenar, J. J. Hillman, B. Saif, and J. Bergstralh, “Acousto-optic imaging spectropolarimetry for remote sensing,” Appl. Opt. 33(31), 7412–7424 (1994). [CrossRef] [PubMed]

10. N. Gupta and V. Voloshinov, “Hyperspectral imager, from ultraviolet to visible, with a KDP acousto-optic tunable filter,” Appl. Opt. 43(13), 2752–2759 (2004). [CrossRef] [PubMed]

11. N. Gupta and V. Voloshinov, “Hyperspectral imaging performance of a TeO2 acousto-optic tunable filter in the ultraviolet region,” Opt. Lett. 30(9), 985–987 (2005). [CrossRef] [PubMed]

12. P. Wang and Z. Zhang, “Double-filtering method based on two acousto-optic tunable filters for hyperspectral imaging application,” Opt. Express 24(9), 9888–9895 (2016). [CrossRef] [PubMed]

13. H. Zhao, Z. Ji, G. Jia, Y. Zhang, Y. Li, and D. Wang, “MWIR thermal imaging spectrometer based on the acousto-optic tunable filter,” Appl. Opt. 56(25), 7269–7276 (2017). [CrossRef] [PubMed]

14. O. I. Korablev, D. A. Belyaev, Y. S. Dobrolenskiy, A. Y. Trokhimovskiy, and Y. K. Kalinnikov, “Acousto-optic tunable filter spectrometers in space missions [Invited],” Appl. Opt. 57(10), C103–C119 (2018). [CrossRef] [PubMed]

15. W. M. Porter and H. T. Enmark, “A System Overview of the Airborne Visible/Infrared Imaging Spectrometer (Aviris),” Proc. SPIE 834, 22–31 (1987). [CrossRef]

16. R. W. Basedow, D. C. Carmer, and M. E. Anderson, “HYDICE system: implementation and performance,” Proc. SPIE 2480, 258–267 (1995). [CrossRef]

17. T. Okamoto and I. Yamaguchi, “Simultaneous acquisition of spectral image information,” Opt. Lett. 16(16), 1277–1279 (1991). [CrossRef] [PubMed]

18. T. Okamoto, A. Takahashi, and I. Yamaguchi, “Simultaneous Acquisition of Spectral and Spatial Intensity Distribution,” Appl. Spectrosc. 47(8), 1198–1202 (1993). [CrossRef]

19. M. Descour and E. Dereniak, “Computed-tomography imaging spectrometer: experimental calibration and reconstruction results,” Appl. Opt. 34(22), 4817–4826 (1995). [CrossRef] [PubMed]

20. M. R. Descour, C. E. Volin, E. L. Dereniak, K. J. Thome, A. B. Schumacher, D. W. Wilson, and P. D. Maker, “Demonstration of a high-speed nonscanning imaging spectrometer,” Opt. Lett. 22(16), 1271–1273 (1997). [CrossRef] [PubMed]

21. J. M. Mooney, V. E. Vickers, M. An, and A. K. Brodzik, “High-throughput hyperspectral infrared camera,” J. Opt. Soc. Am. A 14(11), 2951–2961 (1997). [CrossRef]

22. F. D. Shepherd, J. M. Mooney, T. E. Reeves, P. Dumont, M. M. Weeks, and S. DiSalvo, “Adaptive MWIR spectral imaging sensor,” Proc. SPIE 7055, 705506 (2008). [CrossRef]

23. N. Hagen and M. W. Kudenov, “Review of snapshot spectral imaging technologies,” Opt. Eng. 52(9), 090901 (2013). [CrossRef]

24. Q. Yang, “Static broadband snapshot imaging spectrometer,” Opt. Eng. 52(5), 053003 (2013). [CrossRef]

25. Q. Yang, “Compact static infrared broadband snapshot imaging spectrometer,” Chin. Opt. Lett. 12(3), 031201 (2014). [CrossRef]

26. W. H. Steel, Interferometry (Cambridge University, 1983).

27. J. Kauppinen and V. M. Horneman, “Large aperture cube corner interferometer with a resolution of 0.001 cm^(-1).,” Appl. Opt. 30(18), 2575–2578 (1991). [CrossRef] [PubMed]

28. C. L. Bennett, M. R. Carter, D. J. Fields, and J. A. M. Hernandez, “Imaging Fourier transform spectrometer,” Proc. SPIE 1937, 191–200 (1993). [CrossRef]

29. G. Durry and G. Guelachvili, “High-information time-resolved step-scan Fourier interferometer,” Appl. Opt. 34(12), 1971–1981 (1995). [CrossRef] [PubMed]

30. C. M. Snively, S. Katzenberger, G. Oskarsdottir, and J. Lauterbach, “Fourier-transform infrared imaging using a rapid-scan spectrometer,” Opt. Lett. 24(24), 1841–1843 (1999). [CrossRef] [PubMed]

31. C. Zhang, B. Xiangli, B. Zhao, and X. Yuan, “A static polarization imaging spectrometer based on a Savart polariscope,” Opt. Commun. 203(1), 21–26 (2002). [CrossRef]

32. J. Kauppinen, J. Heinonen, and I. Kauppinen, “Interferometers Based on the Rotational Motion,” Appl. Spectrosc. Rev. 39(1), 99–129 (2004). [CrossRef]

33. R. K. Chan, P. K. Lim, X. Wang, and M. H. Chan, “Fourier transform ultraviolet-visible spectrometer based on a beam-folding technique,” Opt. Lett. 31(7), 903–905 (2006). [CrossRef] [PubMed]

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

35. Q. Yang, “Moving corner-cube mirror interferometer and reflection characteristic of corner-cube mirror,” Appl. Opt. 49(21), 4088–4095 (2010). [CrossRef] [PubMed]

36. Q. Yang, B. Zhao, and D. Wen, “Principle and analysis of a moving double-sided mirror interferometer,” Opt. Laser Technol. 44(5), 1256–1260 (2012). [CrossRef]

37. Y. Ferrec, J. Taboury, H. Sauer, P. Chavel, P. Fournet, C. Coudrain, J. Deschamps, and J. Primot, “Experimental results from an airborne static Fourier transform imaging spectrometer,” Appl. Opt. 50(30), 5894–5904 (2011). [CrossRef] [PubMed]

38. M. W. Kudenov and E. L. Dereniak, “Compact real-time birefringent imaging spectrometer,” Opt. Express 20(16), 17973–17986 (2012). [CrossRef] [PubMed]

39. P. Wang and R. Menon, “Computational multispectral video imaging [Invited],” J. Opt. Soc. Am. A 35(1), 189–199 (2018). [CrossRef] [PubMed]

40. P. B. Fellgett, “Three concepts make a million points,” Infrared Phys. 24(2-3), 95–98 (1984). [CrossRef]

41. P. B. Fellgett, “The nature and origin of multiplex Fourier spectrometry,” Notes Rec. R. Soc. 60(1), 91–93 (2006). [CrossRef]

42. A. Barducci, D. Guzzi, C. Lastri, P. Marcoionni, V. Nardino, and I. Pippi, “Theoretical aspects of Fourier Transform Spectrometry and common path triangular interferometers,” Opt. Express 18(11), 11622–11649 (2010). [CrossRef] [PubMed]

43. P. Connes and G. Michel, “Astronomical Fourier spectrometer,” Appl. Opt. 14(9), 2067–2084 (1975). [CrossRef] [PubMed]

44. T. Hirschfeld, “Fellgett’s Advantage in UV-VIS Multiplex Spectroscopy,” Appl. Spectrosc. 30(1), 68–69 (1976). [CrossRef]

45. P. Luc and S. Gerstenkorn, “Fourier transform spectroscopy in the visible and ultraviolet range,” Appl. Opt. 17(9), 1327–1331 (1978). [CrossRef] [PubMed]

46. A. Barducci, D. Guzzi, C. Lastri, V. Nardino, P. Marcoionni, and I. Pippi, “Radiometric and signal-to-noise ratio properties of multiplex dispersive spectrometry,” Appl. Opt. 49(28), 5366–5373 (2010). [CrossRef] [PubMed]

47. E. Voigtman and J. D. Winefordner, “The multiplex disadvantage and excess low-frequency noise,” Appl. Spectrosc. 41(7), 1182–1184 (1987). [CrossRef]

48. E. A. Stubley and G. Horlick, “A Fourier transform spectrometer for UV and Visible measurements of Atomic emission sources,” Appl. Spectrosc. 39(5), 800–804 (1985). [CrossRef]

49. T. Hirschfeld and D. B. Chase, “FT-Raman Spectroscopy: Development and Justification,” Appl. Spectrosc. 40(2), 133–136 (1986). [CrossRef]

50. D. C. Tilotta, R. D. Freeman, and W. G. Fateley, “Hadamard transform visible Raman spectrometry,” Appl. Spectrosc. 41(8), 1280–1287 (1987). [CrossRef]

51. P. Mouroulis, R. O. Green, and D. W. Wilson, “Optical design of a coastal ocean imaging spectrometer,” Opt. Express 16(12), 9087–9096 (2008). [CrossRef] [PubMed]

52. S. Pacheco and R. Liang, “Snapshot, reconfigurable multispectral and multi-polarization telecentric imaging system,” Opt. Express 22(13), 16377–16385 (2014). [CrossRef] [PubMed]

53. Q. Yang, “Coherent-dispersion spectrometer for the ultraviolet and visible regions,” Opt. Express 26(10), 12372–12386 (2018). [CrossRef] [PubMed]

54. M. Bass, G. Li, and E. V. Stryland, Handbook of Optics (McGraw-Hill, 2010).

	Main advantages of the CDIS
CDIS versus temporal interferometry based on linear motion (e.g. the original moving corner-cube-mirror interferometer)	1. The multiplex disadvantage inherent in ultraviolet-visible interferometry is greatly reduced. 2. The dynamic range requirement of the detector is reduced. 3. Higher spectral resolution for measuring a broadband source in the ultraviolet-visible spectral region.
CDIS versus temporal interferometry based on rotational motion	1. The multiplex disadvantage inherent in ultraviolet-visible interferometry is greatly reduced. 2. The dynamic range requirement of the detector is reduced. 3. High spectral resolution
CDIS versus spatial interferometry	1. The multiplex disadvantage inherent in ultraviolet-visible interferometry is greatly reduced. 2. The dynamic range requirement of the detector is reduced. 3. High spectral resolution
CDIS versus traditional dispersive imaging spectrometer	1. High spectral resolution for a broadband spectral range. 2. The width of the entrance slit has no effect on the spectral resolution.
CDIS versus color filter imaging spectrometer	1. High spectral resolution for a broadband spectral range.

Wavelength	Wave number	Wavelength difference	Wavenumber difference
219.99 nm	45456.6 cm⁻¹
220.00 nm	45454.5 cm⁻¹	220 - 219.99 = 0.01 nm	45456.6 - 45454.5 = 2.1 cm⁻¹
220.01 nm	45452.5 cm⁻¹	220.01 - 220 = 0.01 nm	45454.5 - 45452.5 = 2.0 cm⁻¹
699.9 nm	14287.8 cm⁻¹
700.0 nm	14285.7 cm⁻¹	700 - 699.9 = 0.1 nm	14287.8 - 14285.7 = 2.1 cm⁻¹
700.1 nm	14283.7 cm⁻¹	700.1 - 700 = 0.1 nm	14285.7 - 14283.7 = 2.0 cm⁻¹

separate Interferograms	Wavelength ranges	Wavenumber ranges
interferogram 1	671.30 nm - 700.00 nm	14896.5 cm⁻¹ - 14285.7 cm⁻¹
interferogram 7	551.50 nm - 566.80 nm	18132.4 cm⁻¹ - 17642.9 cm⁻¹
interferogram 35	348.88 nm - 352.56 nm	28663.2 cm⁻¹ - 28364.0 cm⁻¹
interferogram 62	278.74 nm - 280.58 nm	35875.7 cm⁻¹ - 35640.5 cm⁻¹
interferogram 109	219.56 nm - 220.42 nm	45545.6 cm⁻¹ - 45367.9 cm⁻¹

	Main advantages of the CDIS
CDIS versus temporal interferometry based on linear motion (e.g. the original moving corner-cube-mirror interferometer)	1. The multiplex disadvantage inherent in ultraviolet-visible interferometry is greatly reduced. 2. The dynamic range requirement of the detector is reduced. 3. Higher spectral resolution for measuring a broadband source in the ultraviolet-visible spectral region.
CDIS versus temporal interferometry based on rotational motion	1. The multiplex disadvantage inherent in ultraviolet-visible interferometry is greatly reduced. 2. The dynamic range requirement of the detector is reduced. 3. High spectral resolution
CDIS versus spatial interferometry	1. The multiplex disadvantage inherent in ultraviolet-visible interferometry is greatly reduced. 2. The dynamic range requirement of the detector is reduced. 3. High spectral resolution
CDIS versus traditional dispersive imaging spectrometer	1. High spectral resolution for a broadband spectral range. 2. The width of the entrance slit has no effect on the spectral resolution.
CDIS versus color filter imaging spectrometer	1. High spectral resolution for a broadband spectral range.

Wavelength	Wave number	Wavelength difference	Wavenumber difference
219.99 nm	45456.6 cm⁻¹
220.00 nm	45454.5 cm⁻¹	220 - 219.99 = 0.01 nm	45456.6 - 45454.5 = 2.1 cm⁻¹
220.01 nm	45452.5 cm⁻¹	220.01 - 220 = 0.01 nm	45454.5 - 45452.5 = 2.0 cm⁻¹
699.9 nm	14287.8 cm⁻¹
700.0 nm	14285.7 cm⁻¹	700 - 699.9 = 0.1 nm	14287.8 - 14285.7 = 2.1 cm⁻¹
700.1 nm	14283.7 cm⁻¹	700.1 - 700 = 0.1 nm	14285.7 - 14283.7 = 2.0 cm⁻¹

Broadband high-spectral-resolution ultraviolet-visible coherent-dispersion imaging spectrometer

Abstract

1. Introduction

2. Principle

3. Design calculation and numerical simulation

4. Conclusion

Funding

References

Cited By

Figures (9)

Tables (3)

Equations (24)

Optics Express