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Abstract
An advanced Dyson imaging spectrometer in the near ultraviolet-visible-near infrared region was designed, fabricated, and evaluated. A lens with reflective coating on the back surface is applying to replace the traditional lens-reflecting grating combination. The design concept and fabrication and alignment methods as well as the results of evaluations of the proposed spectrometer are described in detail. The advanced imaging spectrometer achieves high resolution in both spectral and spatial direction and low stray light at a high numerical aperture in the working waveband. The performance of this modified porotype is analyzed and evaluated. Results show the spectrometer is well suited for the remote sensing of the ocean color as well as for various agriculture and vegetation-related applications.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Imaging spectrometer is widely used in various fields such as medicine, agriculture, biology and aeronautics and astronautics [1–4]. Compared with spectrometer work in near ultraviolet waveband and visible-near infrared (VIS-NIR) waveband, an NUV-VIS-NIP waveband imaging spectrometer can collect more information.
The primary difficulty in the ocean color observation is that the solar radiation incident on the ocean surface accounts for about 30% of the total radiation after being attenuated by the atmosphere, and only visible light can transmit to the water [5]. In addition, water presents an exponentially decay signal with depth at different rates per wavelength [6]. Therefore, it requires imaging spectrometers with broad spectral range, enough high SNR(signal to noise ratio) and high spectral and spatial resolution.
Concentric structures are well suited for broadband. A variety of configurations of concentric imaging spectrometers have been presented in the past few decades, such as the Offner structure and Dyson structure [7–12]. Offner structure is more popular than Dyson structure, although Dyson structure has better imaging quality, higher energy collection ability and more compact volume, but the slit and image plane in Dyson system is too close to hemisphere lens, it is difficult to place the slit and detector, add the gap between slit/image plane and hemisphere lens will increase spherical aberration.
Many researchers have proposed improvements to the traditional Dyson structure. Montero-Orille [13] analyzed the detailed theory of Dyson spectrometer, proposed an analytical procedure that is based on the removal of astigmatism at two wavelengths. Warren [14] increased the gap between object/image plane and rear surface of hemisphere lens and applied aspheric lens to correct spherical aberration. Pei [15] designed an advanced Dyson spectrometer based on Fery prism to improve energy efficiency and spectral range. Gorp [16] utilized a monolithic lens/prism/mirror combination to replace traditional hemisphere lens and achieved high performance.
In this paper, an advanced Dyson imaging spectrometer is proposed considering the application requirements and the limitations of little space to arrange the slit and detector mechanisms, which has a large field of view (FOV), a wide spectral range with 320-1000nm and a low F number. A lens with reflective coating on the back surface is applying to replace the traditional lens-reflecting grating combination in our design. In order to further increase the distance between the slit and the detector, off-axis system is utilized. At the same time, in order to suppress the spherical aberration and astigmatism, two spherical lenses are split from the original structure. The rest of the manuscript is arranged as follows. In section 2, the theory of aberration for advanced Dyson spectrometer is deduced in detail. Fabrication and alignment of the prototype is analyzed in section 3. In section 4, the tests performance and results evaluation of the prototype imaging spectrometer are discussed. Finally, the conclusions of the study are listed in Section 5.
2. Optical design and analysis of the advanced Dyson spectrometer
2.1 Imaging analysis of the advanced Dyson system with large axial and lateral air spaces
Based on the research of Montero-Orille [17] Traditional Dyson spectrometer is shown in Fig. 1(a), traditional configuration can be divided into three parts. A is a hemispherical lens made of glass, B is air, which can be regarded as a spherical lens with refractive index of 1 and C is a concave grating. Incidence light from entrance slit S will be refracted to the grating G. The emergent light from the diffraction grating will be diffracted into different wavelengths which will be focused on the imaging plane by the hemisphere lens. IM and IS are meridional and sagittal image respectively. Because the refractive index of hemisphere lens is larger than air, so the refraction angle is smaller than incidence angle, which decreases the space between entrance slit and detector. The configuration of advanced Dyson spectrometer described in this paper is shown as Fig. 1(b), the material of part A is replaced with air, and the material of part B is replaced with glass, which means a lens with reflective coating on the back surface is applied to replace traditional configuration. As can be seen in Fig. 1(b), refractive index of B is larger than A, the refract angle θ’ is lager than incident angle θ. Then the distance between slit and detector can be increased.
The optical path in the advanced Dyson spectrometer is shown in Fig. 2, R is radius of the front surface of lens, Rg is radius of grating. A, B and C are hemispherical lens, air and grating respectively in tradition configuration, while they represent air, lens and grating in advanced configuration. The common center of curvature of them is O. θg is diffraction angle of grating which satisfy the grating equation
where g is the grating density, m is the diffraction order, λ is the wavelength. According to the sine rule, we can get where θ is the incident angle from lens to air. The distance between slit and sagittal image can be obtained where θ’ is diffraction angle of lens, which satisfies $n\sin \theta = \sin \theta ^{\prime}$. As shown in Fig. 2, the following relationship of angles can be obtained:Combining above equations, d can be expressed as
emerging from the center of the slit in the advanced Dyson spectrometer.To further magnify the space between slit and detector, we set slit with a perpendicular distance from center of curvature O, the optical path is shown in Fig. 3. We used the same coordinate system as in Ref. [12]. The coordinate system XOgY is established on the symmetric rotation centers of the lens, and the optical system is rotationally symmetric about the X axis.
However, this will cause a small problem, that the slit with perpendicular distance to the X axis will cause the refracted incident chief rays to deviate from the center of the grating. In other words, the center of the stop (also the entrance point O’g of the chief rays) is not the same position as the center of symmetry Og of the grating in the coordinate system XOgY. We established a new coordinate system X’Og’Y’ because the distance between Og and Og’ is so small, the concentric theory is also could still be approximately used in the new coordinate system.
As presentation above, the new coordinate system X’Og’Y’ with the original point Og’ located at the incident point of the chief ray is shown in Fig. 4. Og’ is also seen as the center of the aperture stop. For the new coordinate system X’Og’Y’, when the light passes through various media in the concentric optical system, the relationship between the transverse distance d1 and d’ will still be obey the study of Lobb [18], only with an additional angle γ.
The angle γ can be expressed as
According to sine rule, we can get
According to Fig. 4 and Snell law, the incident angle $\phi $ and refractive angle $\phi ^{\prime}$ can be expressed as
The incident angle i can be obtained by Eq. (7) and Eq. (9)
Grating equation can be expressed as
d’ can be calculated by Eq. (12)Substituting above equations, the equation containing d1, g, λ, R, and Rg will be obtained. The distance d1, R and Rg can be set at first by the mounting requests of the slit and the detector mechanisms. The ruling density g of the grating could be decided according to the request of the spectral resolution. Then we can calculate the other parameters of the whole optical system.
The angles i, $\phi $, $\phi ^{\prime}$, $\gamma $, θg, θ and θ’ can be expressed as functions of d1, when d1=0, Eq. (12) can be reduced to Eq. (5). When d1 increases, it can be seen from the analysis that i, $\phi $, $\phi ^{\prime}$, θg, θ and θ’ increase with d1. It is easy to demonstrate that Rsinθ’ is a monotonically increasing function about d1. The denominator of Eq. (12) can be rewritten as
The cosine terms of Eq. (13) in brackets can be divided into three terms. Then differentiate the first term with respect θ.
As can be seen from Eq. (14), θ’-θ is a monotonically increasing function of θ, and then θ’-θ is a monotonically increasing function of d1. Similarly, $\phi \textrm{ - }\phi ^{\prime}$ is a monotonically increasing function of d1. It is obviously to see that the third term i+θg is a monotonically increasing function of d1. Which means β is a monotonically increasing function of d1. Then cosβ decreases monotonically with d1 when β in range of 0∼π/2. The numerato Rsinθ’ of Eq. (12) increases monotonically with d1 when θ’ in range of 0∼π/2. Which means d’ is a monotonically increasing function of d1. The distance between slit and image can be expressed as d1+d’, and the following relation is obtained
Which means when we set slit with a perpendicular distance from center of curvature O, the space between slit and detector can be magnified.
But this design has two problems, first as can be seen in the Fig. 2, astigmatism of improved Dyson spectrometer is expressed by following equation
If we want to suppress astigmatism, the angle δ should be as small as possible, δ is given by
2.2 Improved analysis for residual aberrations
According to the research by Wynne [19] and Zhang [20], we will adopt a similar method and add variants of the lenses to compensate for residual aberrations. The advanced Dyson spectrometer is splited into three lenses as three spherical lenses based on the principle of equivalent powers of lenses with curvature radius of grating unchanged. The power of lens can be written as [21]
According to Eq. (20), we can calculate the whole optical image distance LM and Ls step by step. Then we impose LM = Ls, to constraint the astigmatism of the system. But Eqs. (19) and (20) cannot be achieved at the same time, so we change the total optical power so that it is not equal to the original, but the change range is within 5%. Which means that we can fine tune the optical power of the original structure, but still satisfy the near concentric structure. Then under the condition of considering astigmatism, we utilize ZEMAX to decide the distribution of the power to suppress spherical aberrations and chromatic aberrations.
2.3 Ray tracing and analysis
The proposed design was analyzed to confirm its feasibility. The material of the three lens is chosen as silica, of which the refractive index n is 1.456 for the selected wavelength 660 nm, a 1024×1024 CCD with pixel size 13µm×13µm is chosen. After the initial parameters are imported into Zemax, the initial parameters are optimized and a system without astigmatism and residual aberrations can be obtained. The optimized parameters of advanced Dyson spectrometer is shown in Table 1. The optimized optical system is shown in Fig. 5.
Table 1. The optimized parameters of advanced Dyson spectrometer
Figure 6(a) presents the footprint diagram in the imaging plane. As can be seen in Fig. 6(a), the effective length of CCD is 8.45mm in spectral direction, which means the number of effective pixels is 650 in spectral direction. Therefore, the spectral sampling was approximately 0.99nm/pixel and the spectral resolution was approximately 3 nm and satisfies the spectral resolution requests. Figure 6(b) shows the spot diagrams for typical wavelength and field of design. From the figure the scale of the spot is less than 13µm over full field of view, and the RMS is less than 2.5µm at wedge field of view, which means the optical system corrects astigmatism well.
Fig. 6. (a) Spectral footprint diagram in imaging plane, (b)Spot diagrams for typical wavelength(320 nm(bule),660 nm(green)),1000 nm(red)).
The modulation transfer function (MTF) of typical wavelength are shown in Figs. 7(a),7(b), and 7(c) the MTFs are over 0.7 at 38.5lp/mm for the full field of view. The RMS spot radii in all the fields are less than 3µm of the working waveband, as shown in Fig. 7(d), which means the optical system achieves high resolution. Figures 7(e),7(f),and 7(g) show that more than 90% energy is encircled within an area of 13µm in radius. Field curvature and distortion are shown in Fig. 7(h), which archives the maximum field curvature is smaller than 0.5 mm, and the maximum distortion is lower than 0.1%. These results demonstrate that the proposed Dyson spectrometer would exhibit excellent imaging performance.
Fig. 7. Simulation results obtained using optimized design: MTF curves for (a) 320 nm, (b) 660 nm, and (c) 1000 nm; (d) RMS spots radii distribution for entire waveband and all fields of view, Diffraction encircled energy (e)320 nm;(f)660 nm;(g)1000 nm;(h)Field curvature in millimeters and distortion in percent (+Y expresses half-length of slit; unit is mm)
2.4 Tolerance and straylight analysis
2.4.1 Tolerance analysis
In order to analyze the feasibility of the machining assembly, tolerance analysis is carried out, and tolerance items such as surface tilt, surface decenter, element tilt, element decenter, and radius are set in Table 2. The diffraction average MTF at 660nm is selected as the evaluation criterion. The major offenders which affect tolerance are listed in Table 3.
Table 2. Tolerances setting in ZEMAX of the calculation
Table 3. Tolerance offenders with most influences on MTF
In all the Monte Carlo sampling calculation for each tolerance concerned, 90% MTF decrease 0.045, 80% MTF decrease 0.038 and 50% MTF decrease 0.015. The decreases in the MTF because of these tolerances were within acceptable limits. Therefore, these tolerances were reasonable and assumed to have a negligible effect on the performance of the prototype.
2.4.2 Stray light analysis
In the advanced Dyson spectrometer, the stray light is mainly multiple-order diffraction from the grating and multiple reflections between the surface of the element. 0, −1, +2 order diffracted lights contain large energy, which is easy to interfere with the required +1order imaging light. The imaging of multiple-order is shown in Fig. 8. light with orders 0 and −1 out of the detector, which would not have direct effect on imaging. However, +2 order diffraction light for wavelengths of 320-500 nm will fall on the imaging plane and have a significant effect on the imaging performance. For multi-level diffracted stray light, we use the following two methods:
- (1) Add a filter in front of the detector to absorb + 2-order diffracted light.
- (2) An antireflection coating larger than 98% for inner wall and light traps are used to avoid other multiple-order diffraction light and multiple reflection stray light.
Fig. 8. Different orders of light on the imaging plane. Three primary wavelengths are presented: 320 nm (blue), 660 nm (green), and 1000 nm (red).
3. Fabrication and alignment
3.1 Optical elements and optomechanical structure
The optomechanical layout of the entire imaging spectrometer is shown in Fig. 9. The main frame was made of type 7A09 aluminum. The telescope and spectrometer structures, including the detector, are independent and attached by the slit to form the imaging spectrometer. Because all the optical elements are made of silica with the exception of the grating (K9), the optomechanical assemblies connecting the mirrors/lenses and the frame are of a titanium alloy (TC4). The optomechanical assembly of the grating is made of Invar. The design could make the structure have excellent mechanical/thermal adaptability for the air remote sensing. Furthermore, the platform in airplane could also decrease the effect of vibration and keep the working temperature at 22 ± 5°C.
Fig. 9. Optomechanical layout of imaging spectrometer,(a)structure of the entire imaging spectrometer (b) profile of the spectrometer (c) prototype of the spectrometer
Off-axis two-mirror telescopes are difficult to fabricate. Therefore, the following processing steps were adopted in this study. First, the mirrors were machined using single-point diamond turning, and the surface precision was monitored with a LUPHO Scan system. Secondly, the full-aperture mirrors were fabricated such that the RMS surface precision was λ/60−λ/70. Finally, precision grinding was performed to remove the extra parts of the mirrors and achieve the final partial off-axis apertures of the mirrors (Fig. 10(a)). This guaranteed that the final surface precision was λ/40−λ/50. The mirrors of the telescope, lenses, and grating of the spectrometer are shown in Fig. 9. The surface precisions of all the lenses and mirrors were better than λ/40.
3.2 Alignment of imaging spectrometer
The aperture stop of the telescope is a virtual stop located between the two mirrors, which are not restricted by the actual mechanism. This was the primary difficulty encountered in the alignment of the imaging spectrometer. Thus, the alignment of the telescope was performed as per the following steps.
- (a) The mirrors were placed into the mounting and cemented using an epoxy resin. Then, the surfaces precisions were tested to ensure they were in the desired range.
- (b) A plane mirror was placed in front of the telescope. The ZYGO interferometer was located at the imaging plane and made to emit a spherical wave. The light traveled through the telescope and was reflected by the plane mirror back through the telescope. By adjusting the telescope, plane mirror, and interferometer, the light was made incident on the interferometer, where it formed an interferogram.
- (c) Based on this interferogram and the related data, the two mirrors were adjusted such that the RMS wavefront map met the wavefront aberration criterion. According to the criterion of Rayleigh, the optical system attains the diffraction limit when the wavefront aberration ≤ λ/14.
- (d) The absence of the actual stop would make the alignment of the system unsymmetrical and result in a locally optimal alignment. Therefore, several sampling symmetrical fields of view were used to solve this problem. The relative locations of the mirrors were adjusted such that the wavefront errors for each pair of the symmetrical fields of view were both reduced and nearly similar. When this was the case for each sampling field of view, it was assumed that the system was aligned.
- (e) All the mountings were fixed, and the wavefront maps were tested to evaluate the final alignment.
Based on the above-described processing steps, a high degree of alignment could be achieved. The RMS wavefront was 0.0704λ in one marginal field of view and 0.072λ in another one. Figure 11 shows the designed wavefront map simulated using Zemax and the corresponding wavefront map tested using the ZYGO interferometer for the same field of view. It can be seen that the two wavefront maps are almost the same.
Fig. 11. Wavefront maps of telescope: (a) simulated in Zemax and (b) tested using ZYGO interferometer.
The alignment of the spectrometer, which was similar that of a common lens group, was relatively easy to achieve, given the lenient tolerances. Once the spectral resolution of the spectrometer met the requirements, the system was considered to be aligned. Finally, the telescope and spectrometer were connected by the slit.
4. Performance assessment
4.1 Spectral performances calibration
The spectral resolution of an imaging spectrometer is its most important parameter. A 405 nm laser with a full width at half maximum (FWHM) of 0.04 nm was used to calibrate the spectral resolution of the fabricated imaging spectrometer. Before the test, the multiple-order diffraction filter was removed, because we wanted to use the 405 nm light and the 2nd-order 810 nm diffraction light to calibrate the spectral resolution and the locations of the different central wavelengths simultaneously. This would help elucidate the relationship between the wavelength and the responsibilities of the detector and ensure that the imaging spectrometer exhibited high precision during use. The test results for the spectral resolution are shown in Fig. 12.
Fig. 12. Spectral resolution test: 405 nm and 810 nm (in red box). Uppermost spectral line is 3rd-order diffraction light of 405 nm, which is out of the actually applied part of the detector.
Figure 12 shows the imaging results for the spectral line in the case of the 405 nm and 810 nm light (the 2nd-order diffraction light of the 405 nm). The FWHM, which are indicative of the spectral resolution, are approximately 3.79 nm and 3.41 nm, separately. Therefore, the spectral sampling is 1.0 nm/pixel at 405 nm and 810 nm. The spectral resolutions were in keeping with the design results. Moreover, the central location of the 405 nm light was at the 1524th pixel while that of the 810 nm light was at the 1134th pixel. Therefore, there were 390 pixels between the central locations of the 405 nm and 810 nm lights, and the average spectral sampling was 1.04 nm/pixel. This also proved that the spectral resolution was uniform in the working waveband. Figure 12 also shows the spectral smile was approximately 1 pixel, which was also in keeping with the design results. Some results of wavelength calibration are in Table 4. The spectral sampling is 0.4 nm.
Table 4. Results of wavelength calibration
It proves that the corresponding center locations and resolutions with the different spectral responses of different wavelengths, were in keeping with expectations confirmed the reliability of the proposed design.
4.2. Radiation calibration
4.2.1 Pixel response nonuniformity calibration
The standard integrating sphere has been utilized to complete the relative radiometric calibration of the prototype. By the observation of the brightness of the integrating sphere. The response curves of different lines have been presented in Fig. 13. The relative differences among all the pixels radiometric responses could be calibrated and corrected. The nonuniformity of the chosen lines can be calculated by Eq. (21).
The nonuniformity of these chosen lines of pixels has been obtained in Table 5.
Table 5. Nonuniformity (N) calibration
4.2.2 Absolute radiation calibration
The absolute radiation calibration experiment have been presented in Fig. 14. By the spectral responses and SVC spectrometer calibrated data, the absolute radiation coefficients of the prototype could be calculated. The results are in Table 6.
Table 6. Absolute radiation calibration results
4.3 Imaging performance
The MTF in different fields of view is an important tool for evaluating the imaging performance. An Optokos MTF tester was used to evaluate the imaging quality of telescope. The video MTFs in the 0°, +8°, −8°, +14°, and −14° fields of view are shown in Fig. 15. The telescope maintained its high imaging performance.
Next, the imaging spectrometer was used in an external field to test its imaging ability. The prototype was placed on a two-dimensional precisely rotating platform. Next, the platform was rotated at a constant speed, and the imaging spectrometer was used to obtain a number of spectral images. The integration time is 50 ms and the time of one total scanning is about 10 s. Figure 16 shows five monochrome images and a fused image from the far vision. These images were obtained at 6 PM and are the original pictures without any corrections. It can be seen that the quality and illumination levels of the images are excellent. Further, the noise levels are low; the stray horizontal lines were formed because of the vibrations of the rotating platform during scanning. These could be removed after using a suitable algorithm. Thus, the imaging results confirmed the high performance of the prototype.
A comparison between the previous instruments and our prototype has been presented in Table 7.
Table 7. Comparison of primary specifications
5. Conclusion
To summarize, we designed, fabricated, and evaluated an improved wideband imaging spectrometer for ocean color remote sensing. The instrument includes a telescope with two off-axis mirrors and an advanced Dyson imaging spectrometer. The space between silt and detector is enlarged by a pair of lens-mirror combination. Furthermore, the lens in the advanced spectrometer is splited into three lenses as three spherical lenses based on the principle of equivalent powers of lenses with curvature radius of grating unchanged to control residual aberrations. The simulation results in Zemax demonstrate that the system can suppress astigmatism over the broadband, while the structure still keep concentric to correct coma aberration. Simulation performance also show that the optical system has low filed curvature and distortions, with filed curvature less than 0.5 mm and distortion of 0.1%. A fast-imaging prototype that exhibits high performance in the 320-1000 nm range was fabricated and tested, thus confirming the feasibility of the proposed design. The further research of the imaging spectrometer will mainly on the following steps: (1) The design will be optimized to decrease the volume and the weight; (2) The grating diffraction efficiency will be increased; (3) More applications will be developed on the airplane.
Funding
Research Starting Foundation for Advanced Talents of Hefei Normal University; High-level introduction of Q1 talent research start-up fund of Hefei Normal University in 2020 (2020rcjj34); Natural Science Foundation of the Education Department of Anhui Province (KJ2020A0109); State Key Laboratory of Rare Earth Resources Utilization (RERU2021003); Teaching and Research Project of Hefei Normal University (2018jy2); Nature Science Research Project of Anhui Province (1908085QE172); Youth Innovation Promotion Association of the Chinese Academy of Sciences (2016203); Instrument Developing Project of Chinese Academy of Sciences (YJKYYQ20190044).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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