A single GLM consists of the upper moveable grating, the silicon dioxide layer, the bottom mirror, and the substrate. The upper moveable grating and bottom mirror, made up of the aluminum, compose a phase grating. Figure 2(a) illustrates the structure of a single GLM. When voltage actuated, the GLM becomes a tunable phase grating device and the optical model is shown in Figure 2(b).

Fourier Optics theory is used to explain the optical principle of a single GLM pixel. The spatially dispersed light shooting on the GLM array in the angle of θ₀, is illuminated in Figure 1(b). The illuminating function of each GLM pixel is as follows: (2) exp ( x , y ) = exp ( j 2 π x f 0 )where f₀=sinθ₀/λ. And the transmittance function of each GLM pixel t_s can be expressed as: (3) t s   ( x , y ) = ( ∑ m = − ∞ ∞ rect ( x + md ′ a ) + e j 4 π h λ   cos   θ 0 ∑ m = − ∞ ∞ rect ( x + md ′ + d ′ / 2 a ) ) rect ( x W ) rect ( y L )where a is the width of upper grating ribbon, m is an integer, d' is the grating constant of GLM, L and W are the length and width of the GLM pixel respectively, h is the distance between upper moveable grating and the bottom mirror, and 4hπ/λcosθ₀ equals to the phase difference between the light reflected from the upper grating and that from the bottom mirror.

The diffraction pattern [13] is seen to be as: (4) U s   ( x ′ , y ′ ) = 1 j λ z   exp ( jkz ) exp [ j k 2 z ( x ′ 2 + y ′ 2 ) ] F ˜ { e ( x , y ) t s   ( x , y ) }where k(equals 2π/λ) is the wavenumber, λ is the wavelength of the incident light, f_x=x/λz, f_y=y/λz, and F̃ represents the Fourier transform operation. Intensity distribution of the diffraction light can be calculated by formula (4): (5) I s   ( x ′ , y ′ ) = | U s   ( x ′ , y ′ ) | 2 = | A λ z T s ( x λ z , y λ z ) | 2

When considering the spectra bandwidth Δλ of the incident light onto each pixel, the intensity of the reflected light onto the detector then can be derived as: (6) I ( x ′ , y ′ ) = ∫ λ n − Δ λ n / 2 λ n + Δ λ n / 2 ( aLW d ′ ) 2 sin   c 2 ( L f y ) ∑ m = − ∞ ∞ sin   c 2 ( am d ′ )   sin   c 2 ( W ( f x − f 0 − m / d ′ ) ) × ( 1 + e j ( m π + 4 h π λ   cos   θ 0 ) ) d λ

Figure 3 illustrates the diffraction pattern of the single grating light modulator calculated by formula (6), where a=5 μm, d'=10 μm, L=50 μm, W=50 μm, λ_n=1,300 nm, Δλ_n=6.25 nm.

Figure 3(a) is the calculated intensity on the detector when the phase difference of GLM is 2mπ, while Figure 3(b) is the intensity when the phase difference of GLM is (2m+1) π. It can be seen that when voltage V_on actuated, the energy of the zero order, almost equaling that of the incident light, reaches maximum, the phase difference is 2mπ and the pixel is on and when a voltage V_off is actuated, the energy reaches nearly zero, when the phase difference is (2m+1) π and the pixel is off. Suppose the reflection efficiency is T, which is the ratio between the intensity of the zero order and the incident light, when the pixel is on, while the reflected ratio is T₀, when the pixel is off. The calculation results derived from formula (6) shows that T and T₀ equals 0.94 and 0.008 respectively. Apparently, the grating light modulator acts as a programmable pixilated optical switch with high contrast.

The GLM array acts as a series of pixilated optical switches in the spectrometer. What is different from large-scale spectrometer is that in handheld MOEMS spectrometer, miniature dimension of optical system, simple instrument structure and cost effectiveness are required. Therefore, the goal of optical design is mainly to ensure there is good spectral resolution in X axis (the dispersive direction), without considering so much about the optical aberration in Y axis. The size of the light spot on a GLM pixel in Y axis is approximately from 500 μm to 800 μm, which is tens of times than that in X axis, and in our sensor, the size of a single GLM is 52 μm×52 μm. Consequently, to better make use of the optical energy in Y axis, 16 grating light modulators in Y direction are used as one pixel column. In other words, a pixel in spectrometer is not a single grating light modulator but a column of them.

The spectrum can be obtained by a string-line pattern scanning along the X-axis direction. The diffracted light shooting on GLM array is shown in Figure 4(a). Essentially, the GLM array is used as a linear array in the spectrometer. Consequently there is no crosstalk [14–15] in its driving circuit, so that will lead to better optical switch performance. The sampling process by GLM array illustrated in Figure 4(b) shows that each pixel can only control a specifically corresponding piece of the incident wavelength band. Both the single near-infrared detector and the GLM array are controlled by a digital signal processor simultaneously. The sampling process can be described as that each pixel is turned on in sequence.

The discrete spectrum by sampling can be derived as: (7) I s   ( λ ) = I ( λ n ) = T × ∫ − ∞ + ∞ I ( λ ) rect ( λ − λ n Δ λ n ) d λ + T 0 × [ ∑ i = 1 n − 1 ∫ − ∞ + ∞ I ( λ ) rect ( λ − λ i Δ λ i ) d λ + ∑ i = n + 1 N ∫ − ∞ + ∞ I ( λ ) rect ( λ − λ i Δ λ i ) d λ ]where N is the number of pixels, Δλ_i is the spectra bandwidth of the incident light on the i^th pixel.

The instrument spectra could be reconstructed using the discrete spectrum obtained by GLM sampling, according to Nyquist–Shannon sampling theorem [16]. As long as the sampling instants are sufficiently close, the spectral signal can be reconstructed accurately. By using a low pass filter, the precise interpolation [16] can be carried out between the sample points. The interpretation of the reconstruction of I(λ) as a process of interpolation becomes evident when we consider the effect in the spectrum signal domain of the low pass filter. The reconstructed instrument spectra can be derived as: (8) I ^ ( λ ) = I s ( λ ) ⊗ r ( λ ) = { T × ∫ − ∞ + ∞ I ( λ ) rect ( λ − λ n Δ λ n ) d λ + T 0 × [ ∑ i = 1 n − 1 ∫ − ∞ + ∞ I ( λ ) rect ( λ − λ i Δ λ i ) d λ + ∑ i = n + 1 N ∫ − ∞ + ∞ I ( λ ) rect ( λ − λ i Δ λ i ) d λ ] } ⊗ sin   c ( λ Ω c ) λ πwhere r(λ) is an ideal low pass filter, Ω_c is the cutoff frequency of the low pass filter.

The spectra detection process was simulated with Matlab. The original spectrum is created by a Gaussian function (peak wavelength is 1,300 nm and the square error is 40,000) as shown in Figure 5(a). Choose the initial parameters as follows: the spectra range is from 900 nm to 1,700 nm, N=128, θ_i=45°, f=50 mm, lg=52 mm, the λ_n and Δλ_n can be acquired from formula (1). Then, according to formula (8), choosing a cubic spline interpolation [17], the reconstructed spectrum can be acquired, shown in Figure 5(b). The average error e[I(n)] can be acquired by calculating the average error of the intensity of each pixel between the original spectrum and the reconstructed spectrum. What can be seen from Figure 5(c) is that the average error is tiny and becomes smaller with the number of pixels increasing. The diffraction ratio T and T₀ of the modulator do not influence the precision of reconstructed spectrum. When the number of pixels is 64, the average error is less than 0.0001. Consequently, the full spectrum can be reconstructed accurately by this method.

To match the size of a diffracted light spot in the miniature spectrometer, the Y axis size of a single GLM should not be too small [18]. However, for a single GLM, the larger the size in the Y axis, the more difficult fabrication would be. Moreover, the difficulty increases exponentially. If we design a GLM of 50 μm × 500 μm size, that is, the size of which in X-axis is 50 μm and that in Y-axis is 500 μm, the stress and temperature during micro processing will cause a worse flatness of the upper movable grating, that would directly lead to a large decrease in the optical switch performance, and even lead the upper movable grating and lower mirror adhere together. Therefore, one effective way is required to make the flatness of upper grating less than λ/10 (λ is the wavelength of incident light) for diffraction elements. For instance, the programmable grating used in digital transform spectrometer proposed by Polychromix, Inc. has a MOEMS grating designed with multi-layer structure to solve this problem. To decrease the cost and complexity of micro processing technology, meanwhile ensure high optical performance and enough optical energy for the spectroscopic sensor, several modulators in a column are used as one pixel and controlled simultaneously in our GLM array device. This new structure of GLM can not only reduce the difficulty of the processing and the operating voltage of the device, but also improve the response speed and flatness of the modulator.

The GLM is fabricated using surface micro-machining technology [19]. The stages of fabrication are as follows: (1) 500 nm–600 nm thick thermal silicon dioxide is deposited by furnace on a <100> p-type silicon wafer, for electrical isolation among bottom electrodes, (2) evaporation of aluminum of 100 nm, (3) lithography of aluminum to form bottom reflector surface and address electrodes, (4) 280 nm thick silicon dioxide dielectric layer was deposited as protection layer by plasma enhanced chemical vapor deposition (PECVD), (5) 600 nm thick aluminum is sputtered, (6) lithography of aluminum to form support posts, (7) polyimide is spin-coated as a sacrificial layer, (8) lithography of vias of posts, (9) evaporation of structural metal layer, (10) 100 nm thick aluminum is evaporated and then lithographed to form the upper moveable grating, (11) release of the sacrificial layer, (12) the grating light modulator has been fabricated.

Figure 7(a) is the scanning electron microscopy photograph of the fabricated GLM array. The dimension of each single modulator is 52 μm × 52 μm and the width of the upper grating ribbon is 4 μm. Figure 7(b) shows the IC package of the grating light modulator array.

To demonstrate the validity of the principle of this kind of spectrometer and to measure the basic characteristics of the spectrometer, an experiment was set up. The architecture of the experimental system is shown in Figure 1(a), above. The experimental device consisted of a tungsten halogen lamp (10 w, Avalight-HAL, Holland), a high pressure mercury lamp (200 w, GY-6, Tuopu Corporation, China), multi-mode optical fiber (100 μm in diameter, numerical aperture is 0.22), a rectangular calibration mirror (focal length equals 5 mm), a plane reflection grating (400 lines/mm), combined Fourier lens (focal length equals 40 mm), a GLM array device, optical stops, a low-noise current amplifier (Stanford model SR560, USA), an oscillograph (Wavepro 7300, USA), an InGaAs detector (the spectrum response range is from 900 nm to 1,700 nm) and a GLM array driving circuit.

According to the analysis above, the precision of the reconstructed spectrum is higher as the number of the pixels increases. Currently, we have fabricated the GLM chip with 32 sampling wavelength points. Through the calibration of three peak wavelength 1,357 nm, 1,367 nm and 1,395 nm which are the characteristic spectrum lines of the high pressure mercury lamp, the detection spectral range of our experimental system is from 1,320 nm to 1,400 nm.