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Abstract
We present the modeling, design and characterization of a compact spectrometer, achieving a resolution better than 1.5 nm throughout the visible spectrum (360–825 nm). The key component in the spectrometer is a custom-printed varied-line-space (VLS) concave blazed grating, where the groove density linearly decreases from the center of the grating (530 g/mm) at a rate of 0.58 nm/mm to the edge (528 g/mm). Parametric models have been established to deterministically link the system performance with the VLS grating design parameters, e.g., groove density, line-space varying rate, and to minimize the system footprint. Simulations have been performed in ZEMAX to confirm the results, indicating a 15% enhancement in system resolution versus common constant line-space (CLS) gratings. Next, the VLS concave blazed grating is fabricated via our vacuum nanoimprinting system, where a polydimethylsiloxane (PDMS) stamp is non-uniformly expanded to form the varied-line-spacing pattern from a planar commercial grating master (600 g/mm) for precision imprinting. The concave blazed grating is measured to have an absolute diffraction efficiency of 43%, higher than typical holographic gratings (~30%) used in the commercial compact spectrometers. The completed compact spectrometer contains only one optical component, i.e., the VLS concave grating, as well as an entrance slit and linear photodetector array, achieving a footprint of 11 11 3 cm3, which makes it the most compact and resolving (1.46 nm) spectrometer of its kind.
© 2017 Optical Society of America
1. Introduction
Compact spectrometers have become increasingly important due to their portability and low cost. Accordingly, they are widely used in chemical analyses, remote sensing of chemicals, and biological research [1, 2]. To miniaturize a spectrometric system, one needs to integrate different optical components into a compact envelope; the most effective way to realize this is to combine reflective (or refractive) and diffractive optical elements to form a new optical element, i.e., a concave grating. A properly designed concave grating not only enables a compact system envelope but also improves the efficiency by reducing the number of required reflections and refractions before the signals reach the photodetector [3, 4].
Conventional compact spectrometers, i.e., Rowland spectrometer [5], employ concave gratings of equidistant grooves and thus the diffracted spectrum will focus on a curved plane, i.e., Rowland circle, resulting in low spectral resolution when pairing with a flat photodetector [5]. To address the issue, one can use a varied-line-spacing (VLS) grating to flatten the projected spectrum, which improves the spectral resolution and minimizes optical aberration [6, 7]. In addition, the VLS grating should be blazed in order to improve the grating efficiency. However, to date there have been no practical and economic solutions to produce blazed VLS gratings on curved substrates. Conventionally, concave gratings are fabricated via mechanical ruling or holographic recording methods [8, 9]. Mechanical ruling cannot produce precise VLS grating due to its limited precision. The holographic recording method can produce precise blazed constant-line-spacing (CLS) gratings on flat substrates by the interference of two planar beams [10]; and produce sinusoidal VLS grating on concave substrates by interfering two spherical beams with compromised diffraction efficiency [11]. With high cost, complex microfabrication processes, e.g., ion-beam etching, can be further applied to the VLS holographic gratings to create the sawtooth grating profiles on substrates of small curvatures [12]. A customizable VLS concave blazed grating of high resolution and good blazing characteristics has yet to be developed.
In this work, we present the modeling, design and characterization of a compact spectrometer based on a custom-printed VLS concave blazed grating, where the VLS pattern is achieved via the non-uniform expansion of a polydimethylsiloxane (PDMS) stamp. The capability to custom-design and precisely produce blazed concave gratings is important for the development of new optical and scientific instruments due to the limited commercially available concave gratings. Section 2 presents the modeling and design of the compact spectrometer as well as the VLS concave grating; Section 3 presents the fabrication and characterization of the VLS concave blazed gratings; Section 4 presents the characterization of the compact spectrometer and discussions.
2. System design
In this section, we present the modeling and design of the VLS concave grating as well as the compact spectrometer. First, design requirements are carefully generated with an aim to develop a high resolution (< 1.5 nm) compact spectrometer operated in the visible range (360 nm to 825 nm). The overall footprint of the device should be less than 12 12 5 cm3. State-of-the-art commercial compact spectrometers, e.g., Torus, Ocean Optics [13], typically have an optical resolution of ~2 nm and a slightly larger system envelope.
Figure 1 presents the optical configuration of the compact spectrometer, which consists of a VLS concave grating, entrance slit and linear photodetector array. The incident light enters the system at the entrance slit A, which can be modeled as a point source. Next, the VLS concave grating disperses and focuses the light to a linear detector array that collects the spatially separated spectrum. The origin O of the coordinate system coincides with the center of the concave grating, which is axisymmetric to the x-axis. The design parameters of the system are summarized in Table 1, where (rA, θA) is the coordinates of the entrance slit; B1(rB1, θB1) and B2(rB2, θB2) are the two ends of the linear photodetector array; H(rH, θH) is the pedal point from point O to the imaging plane. Points A, B1, B2, and H are all on the dispersion plane, i.e., x-y plane. To begin the design, the substrate of the concave grating is first selected with a diameter (D) and radius of curvature (R) of 25.4 mm and 103.4 mm respectively; the slit width (W) is set to be 10 µm. The center groove density is set to be 530 g/mm (i.e., center linewidth d0 = 1886.8 nm), where the grating grooves are parallel to the z-axis. Next, we develop a model based on imaging theories of VLS gratings [14, 15] to optimize the design and predict the best line-space varying rate (α) as well as the location of the linear photodetector array.
Fig. 1 Optical configuration of the compact spectrometer using a custom-printed VLS concave blazed grating
Table 1. Design parameters of the compact spectrometer
First, let P be an arbitrary point on the grating surface. Consider a ray propagating from point A to point B, the optical path difference, i.e., Ψ, between the rays diffracted from point P and point O is:
where N(y, z) is the grating groove number at point P (y, z), m is the diffraction order, and λ is the wavelength. Equation (1) can be expanded into power series:where Fij is the aberration coefficient; and i and j represent the aberration orders related to y and z directions respectively. Mij is a coefficient that depends on the positions of the object and imaging points as well as the shape of the grating substrate. Nij is a coefficient determined by the spatial distribution of the grating grooves. The optimal design is achieved when the sum of aberrations, i.e., I, is minimized at a given wavelength range; this can be mathematically represented by a least square function:The position of the object point A(rA, θA) is set to be (103.0 mm, 15ᴼ). The + 1st diffraction order is used; and the grating spacing, i.e., d, can be expressed as a function of y in Eq. (4):Note that in our design the grating grooves are parallel symmetric to the x-z plane, and the spacing increases linearly with the absolute value of y, where high-order terms of y are omitted. Accordingly, the relationship between N(y) and d(y) can be derived as:Based on Eqs. (1)–(5), the optimal grating line-space varying rate (α) and the imaging position (points H, B1, B2) can be determined. ZEMAX is used to identify and optimize the design parameters; the results are summarized in Table 1. The positions of points B1 and B2 correspond to the spectral lines of 360 nm and 825 nm respectively. The simulated spot diagrams around the wavelengths of 457 nm, 532 nm, and 633 nm are presented in Fig. 2. The corresponding spectral resolution, i.e., full width at half maximum (FWHM), at each wavelength is listed in Table 2. For comparison, we also simulate the spectral resolution of a CLS concave grating of the same configuration. From the results, one may observe that the custom-designed VLS concave grating has an improved spectral resolution of ~15% theoretically. In the following section, we will present how such structures can be precisely fabricated via our custom-built nanoimprinting system.
Fig. 2 Spot diagrams around the selected wavelengths (i.e., 457 nm, 532 nm, and 633nm) at the imaging plane
Table 2. Spectral resolution of the VLS and CLS concave gratings
3. Fabrication and characterization of the VLS concave grating
In this section, we present the (1) fabrication processes of the VLS concave blazed grating via the vacuum nanoimprinting process [16–18]; and (2) characterization of the printed VLS concave grating. For fabrication, first, the selected concave substrate is spin-coated with UV epoxy. Next, a flexible PDMS grating stamp is prepared economically via a commercial planar blazed grating master (Edmund ruled reflective diffraction grating #48462; line density: 600 g/mm; absolute diffraction efficiency: 60%). To begin, a 10:1 weight mixture of PDMS base and curing agent is dispensed onto the quartz grating master and spin-cast at 1,000 rpm; the film is then cured at 70 °C for 10 min. These steps are repeated 4 times to reach a desired stamp thickness of 280 μm, followed by post-baking the PDMS in an 80 °C oven for 3 hours. After that, the PDMS stamp is removed from the master and installed in the vacuum imprinting system [17]. Figure 3(a) illustrates the nanoimprinting process, where the PDMS stamp is inflated (i.e., non-uniformly expanded to form the VLS pattern) to transfer and imprint the grating patterns to the concave substrate via the control of the pressure difference between the top and bottom chambers separated by the PDMS stamp. After UV light exposure, the blazed grating patterns on the concave substrate are formed. Lastly, an aluminum film of 500 nm thick is coated to the grating via e-beam evaporation.
Fig. 3 (a) Illustration of the vacuum imprinting process for fabricating the VLS concave grating; and (b) generation of the VLS grating pattern on the PDMS stamp during its non-uniform expansion process; the specific center linewidth and line-space varying rate can be achieved by controlling the printing pressure and gap distance.
The accuracy of the VLS blazed grating is determined by the precise control of the stamp expansion ratio (K), which determines the local line density of the printed grating. During large membrane deformation, K is a nonlinear function of the membrane’s radial position [19]. To ensure a linear and controllable stamp expansion process, i.e., the line-space varying rate (α) is a constant, we pair the concave substrate (D = 25.4 mm) with a relatively large PDMS stamp (= 100 mm) such that only a small region of the inflated stamp is used to imprint the grating, resulting in a predictable and constant grating line-space varying rate. Practically, K can be precisely controlled by appropriately setting the printing parameters, i.e., imprint pressure (p) and gap distance (g) between the stamp and the concave substrate. As illustrated in Fig. 3(b), adjusting the gap distance and pressure is a direct way to control the expansion ratio (K), and the resulting center groove linewidth (d0) as well as line-space varying rate. Next, we experimentally investigate the relationship between the processing parameters and the imprinting outcome, i.e., d0 and α. As it is difficult to characterize printed features on curved substrates, VLS blazed gratings are printed on planar silicon wafers for the study. The results are summarized in Table 3. From the results, we observe that the center linewidth slowly increases with gap distance when the pressure is held constant (p = 0.5 psi). When the gap distance is held constant (g = 15 mm), the line-space varying rate increases rapidly with the imprint pressure. (Note that both d0 and α are coupled functions of p and g.) The best imprinting parameters for the concave grating may be found through experiments and extrapolation. The parameters used for imprinting the VLS concave grating are p = 0.5 psi and g = 15 mm.
Table 3. VLS grating spacing vs. imprint pressure (p) and gap distance (g)
Figure 4 presents the optical and atomic force microscope (AFM) characterization results of the VLS concave grating. The data confirm the “sawtooth-profile” of the blazed grating has been transferred from the PDMS stamp with a pitch of 1887 nm in the center region of the grating, promising high diffraction efficiency. Figure 5 presents the diffraction test, which is performed with a continuous wave (cw) laser (532 nm; 85.1 mW); the results are summarized in Table 4. From the results, we find the total efficiency reaches ~92%, and the + 1st order (the working order) diffraction has an efficiency of 43.1%, indicating the blazing characteristics of the grating master has been preserved. Note that the efficiency of a holographic grating is ~30% [20]; and the efficiency of the blazed grating master is ~60%.
Fig. 4 Optical and AFM characterization results of the UV imprinted VLS concave blazed grating: (a) printed VLS concave grating (substrate diameter = 25.4 mm; radius of curvature = 103.4 mm); (b) AFM image of the center region in (a); (c) cross-section profile of the white-line indicated in (b); the groove width is measured to be 1887 nm (~530 grooves/mm).
Table 4. Summary of the diffraction test
From the analysis in Section 2, we learn the line density of the VLS concave grating should be high in the center region and gradually decrease towards the edge of the grating; the ideal line-space varying rate (α) is 0.58 nm/mm; when this condition is met, the spectrum from the grating will focus to a flat imaging plane (versus a constant pitch grating), resulting in better optical resolution.
4. System characterization and discussion
Figure 6 presents the experimental setup of the compact spectrometer using the custom-printed VLS grating. The width of the entrance slit is 10 μm in width; the linear photodetector array is Sony ILX511 which has 2048 pixels with an imaging length of 28.6 mm. The system operates the same way as described in the model of Fig. 1, where an incident beam is first projected to the concave grating; then dispersed and focused onto the linear photodetector array for spectral imaging. Three cw lasers of different wavelengths, i.e., diode-pumped solid-state (DPSS) lasers (473 nm and 532 nm) and a helium-neon (HeNe) laser (633 nm), are used to characterize the spectral resolution. The results are shown in Fig. 7 where the FWHM bandwidth is used to define the spectral resolution. Table 5 compares the measured and simulated spectral resolution at each wavelength with a maximum error of ~17.8%. The relatively small error also indirectly proves the precise fabrication of the VLS concave grating. Note that in Fig. 7, the small sidelobes around 633 nm are caused by the imperfect laser beam mode after fiber coupling and grating diffraction, which will not affect the accuracy of the resolution measurement. The differences between the measured and predicted resolution in Table 5 are mainly attributed to the surface profile differences between the model and the actual concave grating, e.g., curvature of the substrate or the line-space varying rate (α).
Fig. 6 (a) Experimental setup for characterizing the spectral resolution; and (b) packaged compact spectrometer with a footprint of 11 × 11 × 3 cm3
Fig. 7 Measured spectrum from the three cw lasers: DPSS laser (457 nm); DPSS laser (532 nm); and HeNe laser (633 nm)
Table 5. Spectral resolution of the compact spectrometer at different wavelengths
Practically, the footprint of the compact spectrometer is determined by the location of entrance slit, the concave grating, and the photodetector shown in the box (white dashed line), as shown in Fig. 6(a). After optimization, the final footprint of the entire system is 11 × 11 × 3 cm3 with a weight of ~230 grams, satisfying our design goals, shown in Fig. 6(b). Table 6 compares our compact spectrometer to a range of state-of-the-art commercial systems that have the same optical configuration. From Table 6, we can conclude that our compact spectrometer has the smallest footprint and best resolution among all blazed gratings-based systems; and has a better efficiency than holographic grating-based systems. The spectral resolution of our system may be further improved (1) by introducing a focusing lens before the linear photodetector at the expense of increasing the system footprint; or (2) by further optimizing the custom-printed VLS grating. It is worth to note that a smaller slit size may improve the spectral resolution by giving away signal strength and increasing the photodetector integration time. Given that the Torus system uses the same photodetector (Sony ILX511) and a smaller entrance slit (5 µm), our compact spectrometer has a better signal-to-noise ratio and faster response time.
Table 6. Comparison between the compact spectrometer and state-of-the-art commercial systems
Table 7 compares the different fabrication techniques of concave gratings, including (1) vacuum imprinting, (2) mechanical ruling, and (3) holographic recording. Overall, the holographic recording method produces sinusoidal gratings of the best resolution (1.04 nm), but suffers from low efficiency (30%). The mechanical ruling method produces blazed gratings of the highest efficiency (60%) at the expense of limited resolution (1.6 nm). The vacuum imprinting method presents a low-cost, high-throughput solution that combines the advantages of both holographic recording and mechanical ruling methods, producing a new class of VLS concave gratings that are both highly resolving (1.46 nm) and efficient (43%) and may help the development of other new optical and spectrometric instruments in the future.
Table 7. Performance comparison of concave gratings fabricated via different techniques
5. Conclusion
We have presented the modeling and design of a miniature spectrometer based on a custom-printed VLS concave blazed grating, achieving a spectral resolution of 1.46 nm and a compact system footprint of 11 × 11 × 3 cm3. A parametric model has been developed to guide the design and fabrication of the VLS concave grating; as well as to optimize the system resolution and minimize the footprint. The VLS concave grating is printed via a custom-built vacuum UV nanoimprinting system, where a PDMS stamp is non-uniformly expanded to form the desired VLS pattern from a planar grating master (600 g/mm) for precision imprinting. The fabricated VLS concave blazed grating is measured to have a center groove density of 530 g/mm, a grating line-space varying rate of 0.58 nm/mm, and an absolute efficiency of 43%, comparable to commercial gratings. The completed compact spectrometer contains only one optical component, i.e., the VLS concave grating, as well as an entrance slit and linear photodetector array, which makes it the most resolving and portable spectrometer of its kind.
Funding
HKSAR Innovation and Technology Commission (ITC), Innovation and Technology Fund (ITF), ITS/129/14; HKSAR Research Grants Council (RGC), General Research Fund (GRF), CUHK 14201214; and National Natural Science Foundation of China (NSFC), Grant 61006076.
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