Abstract:
An optical filter is disclosed including two laterally variable bandpass filters stacked at a fixed distance from each other, so that the upstream filter functions as a spatial filter for the downstream filter. This happens because an oblique beam transmitted by the upstream filter is displaced laterally when impinging on the downstream filter. The lateral displacement causes a suppression of the oblique beam when transmission passbands at impinging locations of the oblique beam onto the upstream and downstream filters do not overlap.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present invention claims priority from U.S. Patent Application No. 61/934,547 filed Jan. 31, 2014, which is incorporated herein by reference. 
     
    
     TECHNICAL FIELD 
       [0002]    The present disclosure relates to optical components, and in particular to optical filters and spectrometers. 
       BACKGROUND 
       [0003]    An optical filter is used to select a spectral band or a spectral component of incoming light. A high pass filter, for example, selects light at wavelengths longer than an edge wavelength of the filter. Conversely a low pass filter selects light at wavelengths shorter than an edge wavelength. A bandpass filter is a distinct type of filter, which selects light at wavelengths proximate to a center wavelength of the filter within a bandwidth of the filter. A tunable bandpass filter is an optical filter, the center wavelength of which may be adjusted or tuned. 
         [0004]    A spectrometer measures an optical spectrum of incoming light. A scanning-type spectrometer may use one or more tunable bandpass filters to select different spectral components of the incoming light. A scanning-type spectrometer operates by scanning the center wavelength of the tunable bandpass filter, so as to obtain the optical spectrum. Alternatively, a polychromator-type spectrometer uses a wavelength-dispersing element optically coupled to a detector array for parallel detection of the optical spectrum. However, conventional optical filters and spectrometers are typically large and bulky, making it a challenge to use them in portable devices and applications. 
         [0005]    In view of the foregoing, it may be understood that there may be significant problems and shortcomings associated with current solutions and technologies for optical filters and spectrometers. 
       SUMMARY 
       [0006]    In accordance with the present disclosure, two or more laterally variable bandpass filters may be stacked at a fixed distance from each other to reduce requirements for impinging beam collimation, or even to completely alleviate the need of a tapered light pipe or another light collimating element. When two laterally variable bandpass filters are stacked together, the upstream filter may function as a spatial filter for the downstream filter. This happens because an oblique beam transmitted by the upstream filter is displaced laterally when impinging on the downstream filter. The lateral displacement may result in suppression of the oblique beam, because transmission wavelengths of the upstream and downstream filters may not overlap when beam impinging locations on the upstream and downstream filters do not overlap, resulting in suppression of oblique beams. Due to this effect, a dependence of spectral selectivity of the optical filter on a degree of collimation of the incoming beam striking the upstream filter may be lessened. 
         [0007]    In accordance with an aspect of the disclosure, there is provided an optical filter comprising an upstream laterally variable bandpass optical filter and a downstream laterally variable bandpass optical filter. The downstream laterally variable bandpass optical filter is sequentially disposed downstream of the upstream variable bandpass optical filter and separated by a distance L along an optical path of an optical beam. The upstream and downstream laterally variable bandpass optical filters each have a bandpass center wavelength that gradually varies in a mutually coordinated fashion along a common first direction transversal to the optical path. A dependence of spectral selectivity of the optical filter on a degree of collimation of the optical beam is less than a corresponding dependence of spectral selectivity of the downstream laterally variable bandpass optical filter on the degree of collimation of the optical beam. 
         [0008]    In one exemplary embodiment, the center wavelengths of the upstream and downstream filters are monotonically e.g. linearly or non-linearly increasing in the first direction. The center wavelengths of the upstream and downstream filters may, but do not have to, have a substantially identical dependence of the bandpass center wavelength on an x-coordinate along the first direction. 
         [0009]    In accordance with the disclosure, there is further provided an optical spectrometer comprising the above optical filter and an optical sensor disposed in the optical path downstream of the downstream laterally variable bandpass optical filter. The optical sensor may include a photodetector array. The downstream laterally variable bandpass optical filter may be in contact with the photodetector array, for a better spectral selectivity. 
         [0010]    In accordance with another aspect of the disclosure, there is further provided a method for obtaining a spectrum of an optical beam propagating along an optical path, the method comprising: filtering the optical beam with an optical filter comprising an upstream laterally variable bandpass optical filter and downstream laterally variable bandpass optical filter, wherein the downstream laterally variable bandpass optical filter is sequentially disposed downstream of the upstream variable bandpass optical filter and separated by a distance L along an optical path of an optical beam, wherein the upstream and downstream laterally variable bandpass optical filters each have a bandpass center wavelength that gradually varies in a mutually coordinated fashion along a common first direction transversal to the optical path, and wherein a dependence of spectral selectivity of the optical filter on a degree of collimation of the optical beam is less than a corresponding dependence of spectral selectivity of the downstream laterally variable bandpass optical filter on the degree of collimation of the optical beam; and detecting optical power distribution along the first direction downstream of the downstream filter. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0011]    Exemplary embodiments will now be described in conjunction with the drawings, in which: 
           [0012]      FIG. 1A  illustrates a conventional linearly variable filter; 
           [0013]      FIG. 1B  illustrates a conventional optical spectrometer based on the linearly variable filter of  FIG. 1A ; 
           [0014]      FIG. 2A  illustrates an optical filter according to the present disclosure, including a pair of laterally variable bandpass filters; 
           [0015]      FIG. 2B  illustrates center wavelength dependences of the laterally variable bandpass filters of  FIG. 2A ; 
           [0016]      FIG. 2C  is a side schematic view of the optical filter of  FIG. 2A  illustrating a principle of spatial filtering by the optical filter; 
           [0017]      FIG. 3  illustrates an optical filter of  FIG. 2A  in a side cross-sectional view showing an acceptance angle of the optical filter; 
           [0018]      FIGS. 4A to 4E  illustrate schematic side views of various embodiments of optical filters of  FIGS. 2A and 3 ; 
           [0019]      FIGS. 5A to 5C  illustrates three-dimensional views of various embodiments of optical filters of the present disclosure; 
           [0020]      FIG. 6A  illustrates schematic cross-sectional side view of a spectrometer including optical filters of  FIGS. 2A ,  3 ,  4 A to  4 E, or  5 A to  5 C and a photodetector array; 
           [0021]      FIG. 6B  illustrates schematic cross-sectional side view of a sealed spectrometer including optical filters of  FIG. 2A ,  3 ,  4 D, or  5 A to  5 C; 
           [0022]      FIGS. 7A to 7D  illustrate partial cross-sectional side views of various embodiments of the spectrometer of  FIG. 6A  showing mounting configurations of the downstream filter on the photodetector array; 
           [0023]      FIG. 8A  illustrates a plan view of a spectrometer embodiment having a tilted two-dimensional (2D) detector array; 
           [0024]      FIG. 8B  illustrates optical power density distribution on different rows of pixels of the 2D detector array of  FIG. 8A ; 
           [0025]      FIG. 8C  illustrates an exploded view of a multi-spectral spectrometer embodiment of the present disclosure; 
           [0026]      FIGS. 9A and 9B  illustrate three-dimensional and side views, respectively, of an optical ray-trace model of optical filters of  FIGS. 2A ,  3 , and  4 B; 
           [0027]      FIG. 10  illustrates a superimposed view of simulated optical power distributions of the optical ray-trace model of  FIGS. 9A ,  9 B at different numerical apertures and distances between upstream and downstream filters; 
           [0028]      FIGS. 11A ,  11 B, and  11 C illustrate simulated detected optical spectra at wavelengths of 1.0 μm, 1.3 μm, and 1.6 μm, respectively; 
           [0029]      FIG. 12  illustrates a simulated dual-line optical spectrum showing a resolving power of the simulated optical filters of  FIGS. 2A ,  3 A- 3 B, and  4 B; 
           [0030]      FIG. 13  illustrates a multi-wavelength spectrum of a simulated spectrometer having the optical filter of  FIG. 2A , shown in comparison with a multi-wavelength spectrum of a simulated spectrometer having a tapered light pipe collimator and a linear variable filter; 
           [0031]      FIG. 14  illustrates simulated spectra of a multi-wavelength light source, obtained with a spectrometer having the optical filter of  FIG. 2A  at different values of the inter-filter distance L; 
           [0032]      FIGS. 15A and 15B  illustrate a plan view ( FIG. 15B ) of a spectrometer of  FIG. 6A ; 
           [0033]      FIG. 16  illustrates monochromatic spectra measured with the spectrometer of  FIGS. 15A and 15B ; and 
           [0034]      FIG. 17  illustrates optical transmission spectra of a doped glass sample measured with the spectrometer of  FIGS. 15A ,  15 B, and compared to a transmission spectrum of the doped glass sample measured with a standard MicroNIR™ spectrometer. 
       
    
    
     DETAILED DESCRIPTION 
       [0035]    While the present teachings are described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives and equivalents, as will be appreciated by those of skill in the art. 
         [0036]    As discussed above, conventional optical filters and spectrometers are large and bulky, which limits their applicability in portable light-sensing devices and applications. Linearly variable filters have been used in spectrometers to provide wavelength separating function. Referring to  FIG. 1A , a conventional linearly variable filter  10  may be illuminated with white light, which includes top  11 , middle  12 , and bottom  13  white light beams. The top  11 , middle  12 , and bottom  13  light beams may strike the linearly variable filter  10  at respective top  11 A, middle  12 A, and bottom  13 A locations. The linearly variable filter  10  may have a center wavelength of a passband varying linearly along an x-axis  18 . For instance, the filter  10  may pass a short wavelength peak  11 B at the top location  11 A; a middle wavelength peak  12 B at the middle location  12 A; and a long wavelength peak  13 B at the bottom location  13 A. 
         [0037]    Referring to  FIG. 1B  with further reference to  FIG. 1A , a conventional spectrometer  19  may include the linearly variable filter  10 , a tapered light pipe  14  disposed upstream of the linearly variable filter  10 , and a linear array  15  of photodetectors disposed downstream of the linearly variable filter  10 . In operation, non-collimated incoming light  16  may be conditioned by the light pipe  14  to produce a partially collimated light beam  17 . The linearly variable filter  10  may transmit light at different wavelengths as explained above with reference to  FIG. 1A . The tapered light pipe  14  may reduce a solid angle of the incoming light  16 , thereby improving spectral selectivity of the linearly variable filter  10 . The linear array  15  of photodetectors may detect optical power levels of light at different wavelengths, thereby obtaining an optical spectrum, not shown, of the incoming light  16 . 
         [0038]    It may therefore be desirable to reduce the size of the spectrometer  19 . The tapered light pipe  14  may often be the largest element of the spectrometer  19 . A collimating element, such as tapered light pipe  14 , may be needed because without it, the spectral selectivity of the linearly variable filter is degraded. This may happen because the linearly variable filter  10  includes a stack of thin dielectric films. The wavelength-selective properties of thin film filters may be generally dependent on the angle of incidence of incoming light, which may deteriorate spectral selectivity and wavelength accuracy of thin film filters. 
         [0039]    Referring to  FIGS. 2A and 2B , an optical filter  20  ( FIG. 2A ) may be provided as described below. For example, the optical filter  20  may include sequentially disposed upstream  21 A and downstream  21 B laterally variable bandpass optical filters separated by a distance L in an optical path  22  of an optical beam  23 . As shown in  FIG. 2B , the upstream  21 A and downstream  21 B filters each may have a bandpass center wavelength λ T  varying in a mutually coordinated fashion along a common first direction  25  represented by the x-axes. The first direction  25  may be transverse to the optical path  22 . By way of a non-limiting example, the bandpass center wavelength λ T  of both the upstream  21 A and downstream  21 B filters of  FIG. 2A  may have respective monotonic, linear dependences  24 A,  24 B, as shown in  FIG. 2B . The center wavelength dependences λ 1T (x) and λ 2T (x) of the upstream  21 A and downstream  21 B filters, respectively, on the x-coordinate may be identical, or shifted with respect to each other e.g. λ 2T (x)=λ 1T (x+x 0 ), where is a constant; or scaled e.g. λ 2T (x)=cλ 1T (x), where c is a constant e.g. 0.9&lt;c&lt;1.1. In other words, the term “coordinated fashion” defines a pre-determined functional relationship between the center wavelength dependences λ 1T (x) and λ 2T (x) of the upstream  21 A and downstream  21 B filters, respectively. 
         [0040]    The configuration of the optical filter  20  may enable a dependence of spectral selectivity of the optical filter  20  on a degree of collimation of the optical beam  23  to be lessened as compared to a corresponding dependence of spectral selectivity of the downstream filter  21 B on the degree of collimation of the optical beam  23 . This performance improvement of the optical filter  20  may result from a spatial filtering effect, which may be understood by referring to  FIG. 2C . In monochromatic light at a wavelength λ 0 , the upstream  21 A and downstream  21 B filters may be approximately represented by slits having “openings”  26  corresponding to locations along the x-axes where the center wavelength λ T =λ 0 . In other words, outside of the “openings”  26 , the upstream  21 A and downstream  21 B filters may be essentially opaque for the monochromatic light at the wavelength λ 0 . The “openings”  26  define an acceptance cone, or solid angle  27  (2θ), which depends on the inter-filter distance L. Any rays outside of the solid angle  27  may be blocked, thus improving the spectral selectivity of the downstream filter  21 B. 
         [0041]    The operation of the optical filter  20  of  FIG. 2A  may be further explained by referring to  FIG. 3  showing the optical filter  20  in a side cross-sectional view. In  FIG. 3 , the first direction  25  may be horizontal, and the center wavelength λ T  may increase from left to right, for both the upstream  21 A and downstream  21 B optical filters. In the example of  FIG. 3 , the bandpass center wavelengths λ T  of the upstream  21 A and downstream  21 B filters may be linearly dependent on the x-coordinate: 
         [0000]      λ T =λ 0   +DΔx   (1)
 
         [0042]    where λ 0  represents a reference bandpass center wavelength at a reference point x 0 , D represents the proportionality coefficient, termed the “slope” of a laterally variable filter, and Δx represents an offset from the reference point x 0 . The slope D may correspond to the slopes of the linear dependences  24 A and  24 B in  FIG. 2B , which may, but does not have to, be identical to each other. Deviations from identical slope of the linear dependences  24 A and  24 B may be advantageous in some applications. 
         [0043]    In the example of  FIG. 3 , the upstream  21 A and downstream  21 B filters may be aligned with each other, so that the reference point x 0  corresponding to the reference bandpass center wavelength λ 0  of the downstream filter  21 B is disposed directly under the reference point x 0  corresponding to the reference bandpass center wavelength λ 0  of the upstream filter  21 A. The upstream filter  21 A may function as a spatial filter for the downstream filter  21 B, defining an angle of acceptance  30  for the downstream filter  21 B. The angle of acceptance  30  may be limited by left  31 L and right  31 R marginal rays at the reference wavelength λ 0 , each propagating at the angle θ to a normal  32  to the upstream  21 A and downstream  21 B filters and striking downstream filter  21 B at the same reference point x 0 . The angle of acceptance  30  may be derived from a passband  33 A of the upstream filter  21 A as follows. 
         [0044]    In the geometry illustrated in  FIG. 3 , the left marginal ray  31 L may strike the upstream filter  21 A at a location x 0 −Δx. Transmission wavelength Δ L  at that location may be, according to Eq. (1), λ L =λ 0 −DΔx. Since the left marginal ray  31 L is at the reference wavelength λ 0 , the left marginal ray  31 L may be attenuated depending on the width of the passband  33 A of the upstream filter  21 A; for sake of this example, e.g. a 10 dB bandwidth is taken to be 2DΔx. Thus, the left marginal ray  31 L may be attenuated by 10 dB. Similarly, the right marginal ray  31 R may strike the upstream filter  21 A at a location x 0 +Δx. Transmission wavelength λ R  at that location may be, according to Eq. (1), λ R =λ 0 +DΔx. The right marginal ray  31 R may also be attenuated by 10 dB. All rays at the reference wavelength λ 0  within the acceptance angle  30  may be attenuated by a value smaller than 10 dB; and all rays at the reference wavelength λ 0  outside the acceptance angle  30  may be attenuated by a value larger than 10 dB. In other words, the upstream filter  21 A may function as spatial filter, effectively limiting the numerical aperture (NA) of incoming light to be separated in individual wavelengths by the downstream filter  21 B. This may result in reduction of the dependence of spectral selectivity of the optical filter  20  in comparison with the corresponding dependence of the spectral selectivity of the single downstream filter  21 B on the degree of collimation of the optical beam  23 . In other words, if the upstream filter  21 A were absent in the optical filter  20 , the spectral selectivity of the optical filter  20  would be much more dependent on the degree of collimation of the optical beam  23 . Typically, the optical beam  23  may result from scattering or luminescence of a sample, not shown, so that the optical beam  23  is not collimated. The lack of collimation of the optical beam  23  in the absence of the upstream filter  21 A would result in worsening of overall spectral selectivity unless a dedicated collimating element, such as a tapered light pipe, is used. Herein, the term “spectral selectivity” may include such parameters as passband width, stray light rejection, in-band and out-of-band blocking, etc. 
         [0045]    For small angles θ, one may write 
         [0000]      θ≈Δ x/L   (2), or
 
         [0000]        L≈Δx/θ   (3)
 
         [0046]    When the space between the upstream  21 A and downstream  21 B filters is filled with a transparent medium having a refractive index n, Eq. (3) becomes 
         [0000]        L/n≈Δx/θ   (4)
 
         [0047]    Eq. (4) may define an approximate relationship between the inter-filter distance L, the refractive index n of the inter-filter gap, a lateral distance Δx along the first direction  25 , related to a bandwidth of the upstream filter  21 A, and the resulting acceptance half-angle θ. A more precise relationship may take into account the wavelength offset due to non-zero angle of incidence, which typically results in a blue shift (i.e. towards shorter wavelength) of the bandpass center wavelength λ T . For instance, the right marginal ray  31 R at the reference wavelength λ 0  striking the upstream filter  21 A at the position x 0 +Δx may be tilted by the angle θ, which shifts the transmission characteristic of the upstream filter  21 A to shorter wavelengths. If this wavelength dependence is to be accounted for, the shoulders of the passband  33 A may shift to the left i.e. shorter wavelengths: 
         [0000]      λ 1 ≈[(λ 0   +DΔx )( n   eff   2 −θ 2 ) 1/2   ]n   eff   (5)
 
         [0048]    where n eff  represents an effective refractive index of the upstream filter  21 A. 
         [0049]    Although in  FIG. 2B , the upstream  21 A and downstream  21 B laterally variable bandpass filters have linearly variable bandpass center wavelengths λ T  as defined by Eq. (1) above, the center wavelengths λ T  of the upstream  21 A and downstream  21 B filters may be monotonically non-linearly, e.g. parabolically or exponentially, increasing or decreasing in the first direction  25 . The dependence of the bandpass center wavelength λ T  on the x-coordinate along the first direction  25  of the upstream  21 A and downstream  21 B laterally variable filters may be identical, or may be different to enable tweaking or varying of the acceptance angle and/or wavelength response of the optical filter  20 . In one embodiment, the bandpass center wavelengths λ T  of the upstream  21 A and downstream  21 B filters may be aligned with each other, such that a line connecting positions corresponding to a same bandpass center wavelength λ T  of the upstream  21 A and downstream  21 B filters forms an angle of less than 45 degrees with the normal  32  to the downstream filter  21 B. For non-zero angles with the normal  32 , the acceptance cone  30  may appear tilted. Thus, it may be possible to vary the acceptance cone  30  direction by offsetting the upstream  21 A and downstream  21 B filters relative to each other in the first direction  25 . Furthermore, the angle may vary along the first direction (x-axis)  25 . 
         [0050]    For a better overall throughput, it may be preferable to have a lateral distance Δx 1  along the first direction  25 , corresponding to a bandwidth of the upstream filter  21 A larger than a corresponding lateral distance Δx 2  along the first direction  25 , corresponding to a bandwidth of the downstream filter  21 B. In one embodiment, the upstream  21 A and downstream  21 B filters each may have a 3 dB passband no greater than 10% of a corresponding bandpass center wavelength λ T . 
         [0051]    The upstream  21 A and/or downstream  21 B filters may include a thin film layer stack including two, three, and more different materials, e.g., high-index and/or absorbing layers may be used to reduce overall thickness of each of the upstream  21 A and downstream  21 B filters. Furthermore, the upstream  21 A and/or the downstream  21 B filters may include diffraction gratings e.g. sub-wavelength gratings, dichroic polymers, etc. 
         [0052]    Referring to  FIG. 4A , the upstream  21 A and downstream  21 B filters of an optical filter  40 A may include thin film wedged interference coatings  41 A and  41 B, deposited on respective substrates  42 A and  42 B joined back-to-back. The substrates  42 A and  42 B may function as a transparent medium having a refractive index n between the upstream  41 A and downstream  41 B thin film wedged interference coatings. Turning to  FIG. 4B , a single common substrate  42  may be used in an optical filter  40 B, the upstream  41 A and downstream  41 B thin film wedged interference coatings being disposed on opposite sides of the common substrate  42 . The common substrate  42  may be wedged as shown in  FIG. 4C , so that the upstream  41 A and downstream  41 B thin film wedged interference coatings (filters) of an optical filter  40 C are disposed at an angle to each other. In this case, the distance L may vary along the first direction  25 . The distance L variation may help one to manage spectral slope mismatch between the upstream  41 A and downstream  41 B filters, as well as spectral linewidth difference between the upstream  41 A and downstream  41 B filters. To that end, the refractive index n may also vary along the first direction  25 , at the distance L constant or varying. 
         [0053]      FIG. 4D  illustrates another configuration of an optical filter  40 D, in which the upstream  41 A and downstream  41 B thin film wedged interference coatings may be facing each other, being disposed in a spaced apart relationship. An optical filter  40 E of  FIG. 4E  illustrates another embodiment including thin film wedged interference coatings  41 A and  41 B both facing a same direction, e.g., the optical beam  23  in this case. 
         [0054]    Referring back to Eq. (4) with further reference to  FIGS. 2A and 4A  to  4 C, the value L/n may typically be greater than 0.2 mm. In one embodiment, the value L/n may be less than 15 mm, e.g., between 0.2 mm and 15 mm. It should be appreciated that the distance L may correspond to a distance between the actual thin film coatings, e.g.,  41 A and  41 B in  FIGS. 4A to 4C , and may include thicknesses of the substrates  42 ,  42 A, and/or  42 B, should these substrates be in the optical path  22  between the thin film coatings  41 A and  41 B. By way of a non-limiting illustration, in the optical filter  40 B of  FIG. 4B , L may represent the thickness of the substrate  42 , and n may represent the refractive index of the substrate  42 . 
         [0055]    Referring now to  FIG. 5A , optical filter  50 A may be similar to the optical filter  20  of  FIG. 2A , and may be similar to the optical filters  40 A to  40 E of  FIGS. 4A to 4E . The optical filter  50 A of  FIG. 5A , however, may further include an aperture  51 A disposed in the optical path  22 . The aperture  51 A may have a width d varying in the first direction  25 . One function of the varying width d of the aperture  51 A may be to adjust the amount of optical energy impinging on the optical filter  50 A, which may be used to compensate for a wavelength dependence of a magnitude of output transmission of the upstream  21 A/downstream  21 B filters, and/or a spectral response of a photodetector array (not shown). 
         [0056]    A compensating filter may be employed for a more precise control of the filter&#39;s spectral response and/or a spectral response of a photodetector, not shown. Referring to  FIG. 5B , optical filter  50 B may be similar to the optical filter  20  of  FIG. 2A , and may be similar to the optical filters  40 A to  40 E of  FIGS. 4A to 4E . A spectral response flattening filter  51 B may be disposed in the optical path  22  of the optical filter  50 B for flattening a spectral response of the optical filter  50 B. Although the spectral flattening filter  50 B is shown in  FIG. 5B  to be disposed on the upstream filter  21 A, the spectral flattening filter  50 B may be disposed on the downstream filter  21 B and/or in the optical path  22  between the upstream  21 A and downstream  21 B filters. 
         [0057]    Turning now to  FIG. 5C , optical filter  50 C may be similar to the optical filter  20  of  FIG. 2A , and may be similar to the optical filters  40 A to  40 E of  FIGS. 4A to 4E . The optical filter  50 C of  FIG. 5C , however, may further include an additional filter  21 C in the optical path  22 . The additional filter  21 C may have a bandpass center wavelength varying in a coordinated fashion with the bandpass center wavelengths of the upstream  21 A and downstream  21 B filters. The additional filter  21 C may also include a high pass or a low pass laterally variable filter, a dispersive element such as a diffraction grating, a coating with spectrally and/or laterally variable absorption, etc. The function of the additional filter  21 C may be to further define input numerical aperture of incoming light, and/or further improve the resolving power of the optical filter  20 . More than three laterally variable bandpass filters  21 A,  21 B, . . .  21 N, where N represents any integer, may be used in the optical filter  50 C. 
         [0058]    Referring to  FIG. 6A  with further reference to  FIG. 2A , an optical spectrometer  60 A ( FIG. 6A ) may include the optical filter  20  of  FIG. 2A  and a photodetector array  61  disposed in the optical path  22  downstream of the downstream filter  21 B. The photodetector array  61  may have pixels  62  disposed along the first direction  25  for detecting optical power levels of individual spectral components of the optical beam  23 , e.g., emitted by a light source  69 . In a broad sense, the term “light source” may refer to a fluorescent or scattering sample, an actual light source, e.g., for absorption measurements, etc. The light beam  23  originating, e.g., from a luminescent and/or scattering sample, may generally include converging or diverging rays. Herein, the term “diverging” may not require that the rays comprising the optical beam  23  originate from a same single point. Similarly, the term “converging” may not require the rays comprising the optical beam  23  to converge to a single point. As explained above with reference to  FIGS. 2C and 3 , the dual-filter structure of the optical filter  20 , including the upstream  21 A and downstream  21 B bandpass laterally variable optical filters, may result in lessening of the dependence of spectral selectivity of the optical spectrometer  60 A on a degree of collimation of the optical beam  23 . In other words, if only the downstream filter  21 B were used, without the upstream filter  21 A, the spectral selectivity of the optical spectrometer may be much more dependent on the degree of collimation of the optical beam  23 , resulting in an overall worsening of the spectral selectivity. 
         [0059]    The photodetector array  61  may be in direct contact with the downstream filter  21 B. The photodetector array  61  may be flooded with a potting material so as to form an encapsulation  63 . One function of the encapsulation  63  may be to provide an electronic and/or thermal insulation of the photodetector array  61 , while not obscuring a clear aperture  64  of the downstream filter  21 B of the optical filter  20 . Another function of the encapsulation  63  may be to protect edges of the upstream  21 A and downstream  21 B filters from impact, moisture, etc. 
         [0060]    Referring to  FIG. 6B  with further reference to  FIGS. 2A and 6A , an optical spectrometer  60 B ( FIG. 6B ) may include the optical filter  20  of  FIG. 2A  and the photodetector array  61  disposed in the optical path  22  downstream of the downstream filter  21 B. The optical spectrometer  60 B may further include an enclosure  66  having a window  67  disposed in the optical path  22  for inputting the optical beam  23 . In the embodiment shown, the window  67  may include the upstream filter  21 A, and the upstream  21 A and downstream  21 B filters are separated by a gap  65  e.g. air gap. The downstream filter  21 B may be mounted directly on the photodetector array  61 . In one embodiment, a small gap, e.g., less than 2 mm, may be present between the downstream filter  21 B and the photodetector array  61 . 
         [0061]    The gap  65  may allow the photodetector array  61  to be thermally decoupled from the enclosure  66 , which in its turn enables deep cooling of the photodetector array  61  by an optional thermoelectric cooler  68 . The enclosure  66  may be hermetically sealed and/or filled with an inert gas for better reliability and environmental stability. A focusing element, not shown, may be provided in the optical path  22  between the downstream filter  21 B and the photodetector array  61  for focusing the optical beam  23  on the photodetector array  61 . A sensor other than the photodetector array  61  may be used. By way of a non-limiting example, a photodetector may be translated relative to the optical filter  20  in the first direction  25 . 
         [0062]    Mounting options of the downstream filter  21 B may include depositing the thin film structure of the downstream filter  21 B directly on the photodetector array  61 . By way of a non-limiting example, in  FIGS. 7A and 7B , the downstream filter  21 B may be deposited on a pixel side  61 A of the photodetector array  61 . In some embodiments, the downstream filter  21 B may be a wedged thin film filter, including two blocking filter sections  71  and a bandpass filter section  72  between the two blocking filter sections  71 . 
         [0063]    In  FIG. 7B  specifically, a light-absorbing mask  73  may be placed between the individual pixels  62 , to shield the individual pixels  62  from stray light. In  FIG. 7C , an alternative mounting option is illustrated: the downstream filter  21 B may be disposed on a back side  61 B of the photodetector array  61 . Of course, this mounting option may require that a substrate  61 C of the photodetector array  61  be transparent to the optical beam  23 . Advantageously, the back-mounting may allow a driver circuitry chip  74  to be flip-chip bonded to the pixel side  61 A of the photodetector array  61 . Turning to  FIG. 7D , the downstream filter  21 B may be segmented by providing, e.g., etching a plurality of parallel grooves  76 , with a black filling material  75  poured into the grooves  76 , the position of which may be coordinated with bars  77  of the light-absorbing mask  73 . 
         [0064]    Referring to  FIG. 8A  with further reference to  FIGS. 6A and 6B , a spectrometer  80 A is shown in a partial plan view. The spectrometer  80 A may be similar to the spectrometers  60 A of  FIG. 6A and 60B  of  FIG. 6B . The spectrometer  80 A of  FIG. 8A , however, may include a two-dimensional (2D) photodetector array  88  having a plurality of individual photodetector pixels  82 . The 2D photodetector array  88  may be rotated, or clocked, by an acute angle α relative to rows  84  of the pixels  82  of the optical filter  20 , so that upon a monochromatic illumination, a spectral line  83  is formed on the photodetector array  31  at the angle α to the rows  84  of the pixels  82  of the 2D photodetector array  88 . Referring to  FIG. 8B  with further reference to  FIG. 8A , the rotation or clocking by the angle α may cause optical power density distributions  85  on different rows  84  of pixels  82  of the 2D photodetector array  88  to be offset from each other. In this manner, instead of one spectrum, a plurality of offset spectra may be obtained, enabling a spectral resolution and wavelength accuracy increase. A signal to noise ratio may also be improved, e.g., by de-convoluting and averaging individual optical power density distributions  85 . 
         [0065]    Turning now to  FIG. 8C , a spectrometer  80 C may be a variant of the spectrometer  80 A of  FIG. 8A . The spectrometer  80 C of  FIG. 8C  may also include the 2D photodetector array  88 . In  FIG. 8C , the 2D photodetector array  88  may or may not be tilted as shown in  FIG. 8A . The spectrometer  80 C of  FIG. 8C  may further include upstream  81 A and downstream  81 B filters similar to the corresponding upstream  21 A and downstream  21 B filters of the optical filter  20  of  FIG. 2A , that is, having bandpass center wavelengths gradually varying in a mutually coordinated fashion along the first direction  25  transversal to the optical path  22  of the optical beam  23 . In  FIG. 8C , the upstream  81 A and downstream  81 B filters each may include a plurality of segments  89 A- 1 ,  89 A- 2 ,  89 A- 3  (the upstream filter  81 A) . . . and  89 B- 1 ,  89 B- 2 ,  89 B- 3  (the downstream filter  81 B) arranged side by side in a second direction  87  perpendicular to the first direction  25 . Each segment  89 A- 1 ,  89 A- 2 ,  89 A- 3  . . . of the upstream filter  81 A corresponds to one of the segments  89 B- 1 ,  89 B- 2 ,  89 B- 3  of the downstream filter  81 B for operation in a dedicated wavelength region. By way of a non-limiting example, the first pair of segments  89 A- 1  and  89 B- 1  may be configured for operation in the wavelength range of 1000 nm to 1200 nm, the second pair of segments  89 A- 2  and  89 B- 2  may be configured for operation in the wavelength range of 1200 nm to 1400 nm, the third pair of segments  89 A- 3  and  89 B- 3  may be configured for operation in the wavelength range of 1400 nm to 1600 nm, and so on. The wavelength ranges may not need to be contiguous. For example, multiple segments may be provided for other wavelength regions such as visible wavelengths or near infrared (IR), mid IR, ultraviolet (UV), and even soft X-ray. Thus, the spectrometer  80 C may be suitable for multi-spectral sensing and/or multi-spectral imaging applications. These multi spectral sending/imaging applications may require suitable substrate and coating materials, as appreciated by those skilled in the art. 
         [0066]    Referring back to  FIG. 2A , a method for obtaining a spectrum of the optical beam  23  propagating along the optical path  22  may include filtering the optical beam  23  with optical filter  20  having upstream  21 A and downstream  21 B laterally variable bandpass optical filters separated by a distance L. As illustrated in  FIG. 2B , the upstream  21 A and downstream  21 B filters each may have a bandpass center wavelength λ T  gradually varying in a mutually coordinated fashion (e.g.  24 A,  24 B) along the common first direction  25  transversal to the optical path  22 . Due to the sequential placement of the upstream  21 A and downstream  21 B filters, a dependence of spectral selectivity of the optical filter, such as bandwidth, out-of-band rejection, etc., on a degree of collimation of the optical beam  23  may be less than a corresponding dependence of spectral selectivity of the downstream filter  21 B alone on the degree of collimation of the optical beam  23 . 
         [0067]    In the next step of the method, the optical power distribution may be detected along the first direction  25  downstream of the downstream filter  21 B. For instance, referring back to  FIGS. 6A ,  6 B, and  8 A, the photodetector array  61  ( FIGS. 6A ,  6 B) or the 2D photodetector array  88  ( FIG. 8A ) may be disposed downstream of the downstream filter  21 B, and the optical power distribution may be detected using the photodetector arrays  61  or  88 . Referring again to  FIGS. 6A and 7A  to  7 C, the downstream filter  21 B may be disposed, e.g. deposited, directly on the photodetector array  61 , which may be flooded with a potting material so as to insulate the photodetector array  61 , while not obscuring the clear aperture  64  of the downstream filter  60 A. 
         [0068]    In some embodiments, a ray-trace simulation may be performed to verify the performance of the optical filter  20 A of  FIG. 2A  and similar filters of the present disclosure. Referring to  FIGS. 9A and 9B , a ray-trace model  90  may include in sequence a Lambertian light source  99 , a rectangular aperture  96 , an upstream laterally variable bandpass filter  91 A, a transparent spacer  92  having the length L, a downstream laterally variable bandpass filter  91 B, and a photodetector  97 . Input parameters of the ray-trace model  90  are summarized in Table 1 below. For example, rays  93  were traced in a sufficient number to obtain repeatable results. Each ray  93  had a pre-defined wavelength and carried a pre-defined optical power. Optical power readings were accumulated in bins of the photodetector  97  aligned along a dispersion direction  95 , which corresponds to the first direction  25  in  FIG. 2A . The constant parameters included the distance from the Lambertian light source  99  to the aperture  96  of 3 mm; size of the photodetector  97  of 6.6 mm×0.25 mm; and number of bins, or pixels, of the photodetector  97  equal to 838. Varied parameters included bandwidth in % and NA in F/# of the upstream  91 A and downstream  91 B laterally variable bandpass filters, and thickness of the transparent spacer  92 . The Lambertian light source  99  emitted light at eight wavelengths of 0.95 μm; 1.05 μm; 1.15 μm; 1.25 μm; 1.35 μm; 1.45 μm; 1.55 μm; and 1.65 μm. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                 Total 
                 Power 
                   
                   
                   
                   
               
               
                   
                   
                 power 
                 density 
                   
                   
                   
                 Distance 
               
               
                   
                 Diffuser 
                 on  
                 on 
                   
                   
                   
                 to 
               
               
                 Model 
                 dimensions 
                 diffuser 
                 diffuser 
                 Upstream 
                 Downstream 
                 L 
                 detector 
               
               
                 # 
                 (L × W mm) 
                 (W) 
                 (W/mm{circumflex over ( )}2) 
                 filter 91A 
                 filter 91B  
                 (mm) 
                 (mm) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 REF 
                  3 × 2.5 
                 100.00 
                 13.33 
                 TLP 
                 TLP 
                 20.0 
                 0.07 
               
               
                 1 
                 10 × 1 
                 133.33 
                 13.33 
                 1.4% LVF 
                 .7% LVF F/#3 
                 1.7 
                 0.07 
               
               
                   
                   
                   
                   
                 F/#3 
                   
                   
                   
               
               
                 2 
                 10 × 1 
                 133.33 
                 13.33 
                 1.4% LVF 
                 .7% LVF F/#3 
                 1.0 
                 0.07 
               
               
                   
                   
                   
                   
                 F/#3 
                   
                   
                   
               
               
                 3 
                 10 × 1 
                 133.33 
                 13.33 
                 1.4% LVF 
                 .7% LVF F/#3 
                 1.7 
                 0.07 
               
               
                   
                   
                   
                   
                 F/#5 
                   
                   
                   
               
               
                 4 
                 10 × 1 
                 133.33 
                 13.33 
                 1.4% LVF 
                 .7% LVF F/#3 
                 1.0 
                 0.07 
               
               
                   
                   
                   
                   
                 F/#5 
                   
                   
                   
               
               
                   
               
             
          
         
       
     
         [0069]    Referring to  FIG. 10 , simulation results are presented in form of optical power distributions accumulated in bins of the photodetector  97  of the optical ray-trace model  90  of  FIGS. 9A ,  9 B. A top graph  100  corresponds to a “reference model”—a simulated commercially available MicroNIR™ spectrometer having a tapered light pipe for light collimation. Plots  101  to  104  correspond to Reference models 1 to 4 respectively of Table 1 above. 
         [0070]    Turning to  FIGS. 11A ,  11 B, and  11 C, a more detailed spectral performance may be simulated at respective wavelengths of 1.0 μm; 1.3 μm; and 1.6 μm. It should be appreciated that Models 1 to 4 illustrated much better wavelength accuracy and similar spectral selectivity. Turning to  FIG. 12 , the resolving power of Models 1 and 3 is demonstrated using a dual spectral line at 1.3 μm, at 0.12 μm separation. It should be appreciated that in the results shown in  FIGS. 10 ,  11 A to  11 C, and  FIG. 12 , Models 1 to 4 did not have a tapered light pipe or another light collimating elements, yet the Models 1 to 4 have shown an acceptable spectral bandwidth. When the tapered light pipe is excluded from the reference model, the spectral selectivity of the reference model becomes unacceptably low. 
         [0071]    Table 2 below summarizes the obtained simulated performance of Models 1-4. 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                   
                 Power 
                   
                   
               
             
          
           
               
                   
                 Peak  
                 Peak  
                 Peak  
                   
               
               
                   
                 Irrad. 
                 Irrad. 
                 Irrad. 
                 Resolution 
               
             
          
           
               
                   
                 @ 
                 @ 
                 @ 
                 1.0 μm 
                 1.3 μm 
                 1.6 μm 
               
               
                 Model 
                 λ = 1.0 μm 
                 λ = 1.3 μm 
                 λ = 1.6 μm 
                 wave- 
                 wave- 
                 wave- 
               
               
                 # 
                 (W/m{circumflex over ( )}2) 
                 (W/m{circumflex over ( )}2) 
                 (W/m{circumflex over ( )}2) 
                 length 
                 length 
                 length 
               
               
                   
               
             
          
           
               
                 REF 
                 7.6 
                 16.7 
                 12.2 
                 9 
                 11 
                 17 
               
               
                 1 
                 2.8 
                 9.9 
                 15.9 
                 8 
                 12 
                 15 
               
               
                 2 
                 4.3 
                 14.5 
                 21.3 
                 9 
                 13 
                 15 
               
               
                 3 
                 5.1 
                 11 
                 15.9 
                 5 
                 9 
                 12 
               
               
                 4 
                 8.6 
                 17.5 
                 25.5 
                 7 
                 12 
                 13 
               
               
                   
               
             
          
         
       
     
         [0072]    Performance of the optical filter  60 A of  FIG. 6A  may be verified by simulation. Performance of a standard MicroNIR™ spectrometer containing aperture boot, tapered light pipe, InGaAs diode array, was also simulated to provide a reference. Turning to  FIG. 13 , the standard MicroNIR™ spectrometer performance may be represented by dashed-line spectrum  131  of a multi-wavelength signal between 0.9 μm and 1.7 μm separated by 0.1 μm. Solid-line spectrum  132  illustrates the simulated performance of the spectrometer  60 A, which is free of any collimating or light shaping optics. Some stray light between the spectral peaks is attributed to the coating, which has not been optimized for the wavelength range used. The illumination conditions for both measurements were identical. 
         [0073]    Referring to  FIG. 14 , multi-wavelength spectra  140 A- 140 G were obtained by simulation using the optical filter  20  of  FIG. 2A  at different values of the inter-filter distance L ranging from 0.2 mm to 30 mm. It should be appreciated that, as the inter-filter distance L increases, the filter throughput decreases, and the out-of-band rejection of stray light  141  improves. This may happen because as the inter-filter distance L increases, the acceptance cone 2θ of the optical filter  20  ( FIGS. 2C ,  3 ) is reduced. 
         [0074]    Turning to  FIG. 15A , a spectrometer  150  may include a housing  151  having a window  152 . A optical filter  153  may include an upstream laterally variable filter, not shown, physically spaced at 2.08 mm from a downstream laterally variable filter, not shown. The upstream filter, not seen in  FIG. 15A , may have the passband of 1.3% of the center wavelength of 1300 nm and 900 nm to 1700 nm range. The upstream filter at the top of the optical filter  153  may have a width of 2 mm, a length of 8 mm, and a thickness of 1.1 mm. The downstream filter may have the passband of 0.8% of the center wavelength of 1300 nm and 900 nm to 1700 nm range. The downstream filter may have a width of 1.4 mm, a length of 7.4 mm, and a thickness of 1.5 mm. A standard 128-pixel detector array, not shown, was placed 80 micrometers away from the downstream filter. An electronic driver  154  was used to driver the detector array. 
         [0075]    The optical filter  153  and the electronic driver  154  may also be seen in  FIG. 15B , which is a magnified view of  FIG. 15A , as symbolically shown with solid lines  155 . As shown in  FIG. 15B , a scale bar  156  having a length of 5 mm may be used. 
         [0076]    Referring now to  FIG. 16 , emission spectrum  161  and  162  were obtained using the spectrometer  150  of  FIGS. 15A and 15B . Emission of two laser sources at wavelengths of 1064 nm and 1551 nm was directed, in turn, onto an integrating sphere to create a lambertian illumination source with a switchable emission wavelength. Integration times of the photodetector array were adjusted, so both spectra had the same peak amplitude, because each laser had different power output levels. No other spectral or spatial filters were used for these measurements. The integration sphere had a 25 mm port and was placed 35 mm away from the upstream filter. In both spectra  161  and  162 , the wavelength resolution may be limited by the pixel structure of the photodetector array. The instrumental 3 dB bandwidth at 1065 nm may be estimated to be 1.2%·1065 nm=12.8 nm. The instrumental 3 dB bandwidth at 1550 nm may be estimated to be 0.82%·1550 nm=12.7 nm. 
         [0077]    Turning to  FIG. 17 , transmission spectra  171  and  172  were obtained using a NIST traceable transmission reference (in this case an Avian doped glass reference WCT2065-025) placed in front of a halogen lamp. The first spectrum  171 , shown in solid line, was obtained using the spectrometer  150  of  FIGS. 15A and 15B . The second spectrum  172 , shown in dotted line, was obtained using a standard MicroNIR1700 spectrometer manufactured by JDS Uniphase Corporation, Milpitas, Calif., USA. 
         [0078]    In both cases, dark-state reference spectra were collected by blocking the light source. White-state reference spectra were collected by removing the doped glass reference from the optical path. One can see that the first spectrum  171  is closely correlated with the second spectrum  172 . The first spectrum  171  was obtained with a 1 mm wide aperture placed in front of the spectrometer  150  of  FIGS. 15A and 15B . Without the aperture, the resolution was slightly reduced, but the integration (data collection) time decreased by a factor of three. 
         [0079]    In the preceding specification, various embodiments have been described with reference to the accompanying drawings. It will, however, be evident that various modifications and changes may be made thereto, and additional embodiments may be implemented, without departing from the broader scope of the disclosure as set forth in the claims that follow. The specification and drawings are accordingly to be regarded in an illustrative rather than restrictive sense. 
         [0080]    At this point it should be noted that an optical filter and spectrometer in accordance with the present disclosure as described above may involve the processing of input data and the generation of output data to some extent. This input data processing and output data generation may be implemented in hardware or software. For example, specific electronic components may be employed in a processor, module, or similar related circuitry for implementing the functions associated with providing an optical filter and/or a spectrometer in accordance with the present disclosure as described above. Alternatively, one or more processors operating in accordance with instructions may implement the functions associated with the present disclosure as described above. If such is the case, it is within the scope of the present disclosure that such instructions may be stored on one or more processor readable storage media (e.g., a magnetic disk or other storage medium), or transmitted to one or more processors via one or more signals embodied in one or more carrier waves. 
         [0081]    The present disclosure is not to be limited in scope by the specific embodiments described herein. Indeed, other various embodiments and modifications, in addition to those described herein, will be apparent to those of ordinary skill in the art from the foregoing description and accompanying drawings. Thus, such other embodiments and modifications are intended to fall within the scope of the present disclosure. Further, although the present disclosure has been described herein in the context of a particular implementation in a particular environment for a particular purpose, those of ordinary skill in the art will recognize that its usefulness is not limited thereto and that the present disclosure may be beneficially implemented in any number of environments for any number of purposes. Accordingly, the claims set forth below should be construed in view of the full breadth and spirit of the present disclosure as described herein.