Abstract:
A tunable ultra-compact spectrometer and methods for spectrometry therefor can include a single pixel and a Fresnel zone plate having a focal length at a first temperature T 1  and a first wavelength λ 1 , and a focal point. The pixel can be twenty micrometers square and can be placed at a distance from the pixel that equal to the focal length so that the focal point is at the pixel. The Fresnel zone plate can be made of a material that causes the same focal point at the pixel at T 2 , but at a different wavelength λ 2  than wavelength λ 1 . A heat source can selectively add heat to the Fresnel zone plate to cause a second temperature T 2 . Exemplary materials for the Fresnel zone plate can be quartz for visible wavelengths, silicon for infrared wavelength, or other materials, according to the λ(s) of interest.

Description:
FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT 
     The United States Government has ownership rights in this invention. Licensing inquiries may be directed to Office of Research and Technical Applications, Space and Naval Warfare Systems Center, Pacific, Code 72120, San Diego, Calif., 92152; telephone (619) 553-5118; email: ssc_pac_t2@navy.mil, referencing NC 103643. 
    
    
     FIELD OF THE INVENTION 
     The present invention pertains generally to spectrometers. More specifically, this invention pertains to ultra-compact spectrometers. The invention is particularly, but not exclusively, useful as an ultra-compact spectrometer that can incorporate a Fresnel zone plate and a single pixel to function as the spectrometer. 
     BACKGROUND OF THE INVENTION 
     A spectrometer is a device to measure the wavelength or frequency components of the electromagnetic spectrum. Most optical spectrometers use a diffraction grating or a prism in order to disperse light, where the spectrum of light is separated in space by wavelength. Spectrometers are frequently utilized for environmental or chemical analysis, fluorescence or Raman measurements. 
     Fresnel zone plates are circular diffraction gratings with radially increasing line density. The radially symmetric rings alternate between opaque and transparent zones. The zones can be spaced so that the diffracted light constructively interferes at the desired focus, creating an image there. Fresnel zone plates behave like a circular lens with focusing behavior which approximates that described by the thin lens formula 1/p+1/q=1/f, where p is the object distance, q is the image distance, and f is the focal length. The main difference between a lens and a zone plate is that the zone plate has different diffraction orders and therefore several focal spots, as opposed to just one focal spot (focal point) for a lens. 
     In view of the above, it can be an object of the present invention to provide an ultra-compact spectrometer that can fit on a single pixel. Yet another object of the present invention can be to provide an ultra-compact spectrometer that can take advantage of thermal expansion properties of a Fresnel zone plate to provide an indication of a presence of a wavelength, using a single pixel. Still another object of the present invention can be to provide a thermally tunable chip scale, ultra-compact, 20 μm diameter or less spectrometer. Another object of the present invention can be to provide an ultra-compact spectrometer that can be relatively easy to manufacture and that can be used in a cost-effective manner. 
     SUMMARY OF THE INVENTION 
     A tunable ultra-compact spectrometer and methods for spectrometry therefor according to several embodiments of the present invention can include a single pixel and a Fresnel zone plate. The Fresnel zone plate can have a focal length that focuses radiation at a first wavelength λ 1  and a first temperature T 1  at a focal point. The pixel can be square and can have dimensions of less than twenty micrometers (L=20 μm) by twenty micrometers (L=20 μm). The Fresnel zone plate can be placed at a distance from the pixel that can be equal to the focal length so that the focal point is at the pixel. 
     The spectrometer and methods can further incorporate a heat source for selectively adding heat to the Fresnel zone plate to a second temperature T 2 =T 1 +ΔT. The Fresnel zone plate can be made of a material having thermal expansion properties, which can cause the same focal point at the same pixel at T 2 , but at a different wavelength λ 2  than wavelength λ 1 . If λ 1  and λ 2  are optical wavelengths, the Fresnel zone plate can be made of glass, quartz, or sapphire. If λ 1  and said λ 2  are infrared wavelengths, the Fresnel zone plate can be made of silicon, germanium and semiconductor alloys. Other materials could be used, depending on the λ(s) of interest. 
     The heat source can further add heat to the Fresnel zone plate at increments of ΔT, to establish a plurality of Fresnel zone plate temperatures T 2 =T 1 +ΔT through T n =T 1 +(n−1) ΔT. The plurality of temperatures T 1  through T n  can establish a corresponding plurality of wavelengths λ 1  through λ n , at the same pixel. In several alternative embodiments, a plurality of pixels can be arranged as a two-dimensional array, and a plurality of Fresnel zone plates of different materials can be provided, but at the same focal length, with each Fresnel zone plates corresponding to one of the pixels and establishing a plurality of corresponding focal points on different pixels at different wavelengths λ n  of interest, but at the same focal length. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The novel features of the present invention will be best understood from the accompanying drawings, taken in conjunction with the accompanying description, in which similarly-referenced characters refer to similarly-referenced parts, and in which: 
         FIG. 1  is a top plan view of a prior art Fresnel zone plate; 
         FIG. 2  is a top plan diagram of an expandable Fresnel zone plate that can be made of a material with known thermal expansion properties, prior to expansion; 
         FIG. 3  is a top plan diagram of the same Fresnel zone plate of  FIG. 2 , after thermal expansion; 
         FIG. 4  is a diagram of the Fresnel zone plate of  FIG. 3 , which illustrates the effects of the expansion at the wavelength being focused for a given focal length; 
         FIG. 5  is a block diagram of the ultra-compact spectrometer of the present invention according to several embodiments; 
         FIG. 6  is a schematic which shows the effect of the device of  FIG. 5  on the wavelength of light focused a pixel of the pixel plane; 
         FIG. 7  is the same as  FIG. 6  a plan view of the pixel plane during operation of the device, as heat is added to the Fresnel zone plate of the spectrometer of  FIG. 5 ; and, 
         FIG. 8  is a block diagram that is illustrative of steps that can be taken to accomplish the methods of the present invention according to several embodiments. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     In brief overview, a pixel can be thought of as a device to measure the wavelength or frequency components of the electromagnetic spectrum. Most optical spectrometers use a diffraction grating or a prism in order to disperse light, where the spectrum of light is separated in space by wavelength. Spectrometers are frequently utilized for environmental or chemical analysis, fluorescence or Raman measurements. 
     Referring initially to  FIG. 1 , a prior art Fresnel zone plate is shown and is generally designated with reference character  10 . As shown in  FIG. 1 , prior art Fresnel zone plates  10  can have circular diffraction gratings with radially increasing line density. The radially symmetric rings  12  (rings  12   1 ,  12   2 ,  12   3  and  12   4  are shown in  FIG. 1 ) can alternate between opaque zones  14  (cross-hatched in  FIG. 1 ) and transparent zones  16   i  (zone  16   1  is shown in FIG.  1 ). The zones  14 ,  16  can be spaced so that the diffracted light constructively interferes at the desired focus, creating an image there. Thus, Fresnel zone plates can behave like a circular lens with focusing behavior which approximates that described by the thin lens formula in Equation (1):
 
1/ p+ 1/ q= 1/ f,   (1)
 
where p is an object distance, q is an image distance, and f is a focal length. The main difference between a lens and a zone plate is that the zone plate can have different diffraction orders and therefore several focal spots.
 
     The Fresnel zone plate focal length “f” can be given by Equation (2): 
                   f   =       r   n   2       n   ⁢           ⁢   λ               (   2   )               
Where r n  is the radius of the outermost ring, n is the number of rings  12  in  FIG. 1 , and λ is the wavelength. This result shows that each source wavelength has a different focal length. Furthermore, λ and f are inversely related; for a given zone plate, long wavelengths will focus more quickly than short wavelengths. The zone plate radius can be directly related to the zone plate resolution “w”, Equation (3):
 
                   w   =       λ   ⁢           ⁢   f       2   ⁢           ⁢     r   n                 (   3   )               
The number of zones n in Equation (2) above can have an inverse square relation to the resolution; therefore, doubling the resolution of a zone plate while preserving its focal length requires a quadrupling of the number of zones. This can be described by Equation (4):
 
     
       
         
           
             
               
                 
                   n 
                   = 
                   
                     
                       λ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       f 
                     
                     
                       4 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         w 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Referring now to  FIGS. 2 and 3 ,  FIG. 2  illustrates a tunable Fresnel zone plate, which can be made of metal, a metal alloy, or a material with a large thermal expansion coefficient. The tunable Fresnel zone plate can takes advantage of the thermal expansion properties that the material that the Fresnel zone plate can be is made of. For this specification, a Fresnel zone plate can be thought of as tunable when it is constructed with known dimensions, and with a known thermal expansion coefficient, so that the addition of a predetermined amount of heat will cause the Fresnel zone plate  10  to change dimensions by a known amount, to “tune”, or cause a refocusing of radiation at different focal lengths f, or at the same focal length f but at a different wavelength λ. 
     Referring now to  FIG. 3 ,  FIG. 3  is the same Fresnel zone plate  10  of  FIG. 2  but after heat addition and thermal expansion. The arrow  18  can indicate the direction of thermal expansion. For example, an as shown in  FIG. 3 , transparent zone  16   1  can expand radially outward into transparent zone  16   1 ′, and opaque zone  14   3  can expand radially outward into opaque zone  14   3 ′. In general, linear thermal expansion of materials can be governed by Equation (5):
 
Δ T=L·ΔT·α   (5)
 
Where ΔT is the change in temperature (in degrees Celsius), L is the length of the material, and a is the linear thermal expansion coefficient of the material. Table 1 below is an example of a list of large thermal expansion coefficients, as known in the prior art (taken from Chapter 17, Laser and Optics User&#39;s Manual Agilent, ©2002). It should be appreciated, however, that other references could be used, and lists and tabulations of thermal expansion coefficients are well known in the prior art, and can be found for reference and incorporation into the present invention without undue experimentation. Generally, the greater the thermal expansion coefficient α, the more responsive the Fresnel zone plate  10  will be to the addition/removal of heat, in terms of expansion and contraction.
 
     
       
         
               
             
               
               
               
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Pure Metals And Their Linear Thermal Expansion Coefficient 
               
             
          
           
               
                   
                 Alloys 
                 Coefficient of Expension 
                   
               
             
          
           
               
                   
                 PURE METALS 
                 ppm/° C. 
                 ppm/° F. 
               
               
                   
               
             
          
           
               
                   
                 Beryllium 
                 11.6 
                 6.5 
               
               
                   
                 Cadmium 
                 29.8 
                 16.6 
               
               
                   
                 Calcium 
                 22.3 
                 12.4 
               
               
                   
                 Chromium 
                 6.2 
                 3.5 
               
               
                   
                 Cobalt 
                 13.8 
                 7.7 
               
               
                   
                 Gold 
                 14.2 
                 7.9 
               
               
                   
                 Iridium 
                 6.8 
                 3.8 
               
               
                   
                 Lithium 
                 56.0 
                 31.0 
               
               
                   
                 Manganese 
                 22.0 
                 12.3 
               
               
                   
                 Palladium 
                 11.76 
                 6.6 
               
               
                   
                 Platinum 
                 8.9 
                 5.0 
               
               
                   
                 Rhenium 
                 6.7 
                 3.7 
               
               
                   
                 Rhodium 
                 8.3 
                 4.8 
               
               
                   
                 Ruthenium 
                 9.1 
                 5.1 
               
               
                   
                 Silicon 
                 5.0 
                 2.8 
               
               
                   
                 Silver 
                 19.68 
                 11.0 
               
               
                   
                 Tungsten 
                 4.6 
                 2.7 
               
               
                   
                 Vanadium 
                 8.3 
                 4.6 
               
               
                   
                 Zirconium 
                 5.85 
                 3.3 
               
               
                   
               
             
          
         
       
     
     Tuning the Fresnel zone plate radius by thermal expansion can have an effect on the focal length as well as the wavelength which comes into focus, Equation (6): 
                   f   =       r   n   2       n   ⁢           ⁢   λ               (   6   )               
In view of the above, it can be appreciated that the tunable Fresnel zone plate may be formed on a substrate with one or more heating and/or cooling elements, and if desired monolithically integrated control circuitry, to effect a desired focal length by changes in the temperature to exploit the variable coefficients of expansion and thus form a tunable focusing lens.
 
     Referring now to  FIG. 4 , the effects of a heating an expandable Fresnel zone plate while referencing the same focal length f and same focal point p focal  can be shown. As shown in  FIG. 4  prior to expansion, the tunable Fresnel zone plate  10  can focus green light  17  (λ=532 nm) at focal point p focal  and at a distance equal to focal length f when the plate  10  is heated to temperature T 1 . An amount of heat equal to ΔT can then be added to tune Fresnel zone plate  10 , to increase the temperature to T+ΔT. After expansion, the tunable Fresnel zone plate  10  can focus red light  19  (λ=632 nm) at the same distance (focal length f and focal point p focal ). 
     Referring now to  FIG. 5 , the ultra-compact spectrometer of the present invention according to several embodiments can be shown, and can be designated with reference character  20 . As shown, spectrometer  20  can include a Fresnel zone plate  22  and a heat source  24  in thermal communication with the Fresnel zone plate  22 . Spectrometer can further include at least one pixel  26  within a pixel planar array  28 . Pixel  26 /array  28  can be spaced apart from Fresnel zone plate  12  by a focal length  30 . 
     As incoming radiation  32  impinges on zone plate  22 , Fresnel zone plate  22  can function as a lens and can focus the radiation onto pixel  26 . If the Fresnel zone plate is made of a material is prone to thermal expansion, and the expansion coefficient is known, this property can be taken advantage of to establish a tunable Fresnel zone plate  22 . The tunable Fresnel zone plate can then focus the radiation  32  at a single focal point p focal . Heat can be selectively added to (or removed from) Fresnel zone plate  12  by heat source  14  in response to non-transitory written instructions incorporated into processor  34 . The amount of heat that is selectively added can cause the wavelength of light that is focused at focal point to change. Pixel  26 /array  28  can provide an indication of the presence (or not) of radiation  32  on pixel  26  to processor  34 . Processor can receive an input the indication from pixel  26  and temperature T of Fresnel zone plate to provide an output indication of the presence of a particular wavelength λ in the radiation  32 , to thereby function as a spectrometer. 
     From the above, it can be seen that the ultra-compact spectrometer  20  and the tunable Fresnel zone plate  22  can be tuned over a wide range of wavelengths for spectroscopy. The spectrometer  20  can function with only a single pixel  26  (a 20 μm×20 μm square) could be used for readout, and thus can offer an extreme reduction in the size of the spectrometer. Both devices may be formed with materials compatible with microfabrication techniques and thus may be batch fabricated and the economy of scale will offer reduced cost per device. The symmetry of the device minimizes misalignment with linearly polarized light. 
     Still further, choice of materials compatible with microfabrication techniques will allow formation of arrays of tunable Fresnel zone plates of different materials. Each Fresnel zone plate can be oriented to a corresponding pixels  26  in an array  28 , but spaced potentially with independently controlled responses, to provide a simultaneously indication of a plurality of wavelengths of interest. In this manner, differential temperature measurement may also be used by have paired Fresnel zone plates constructed with materials of differing thermal expansion coefficients. The tunable ultra-compact spectrometer may use alternative 2D arrayed sensors as opposed to a CCD array. Alternate detectors may, for example, include low cost photodiode arrays or active-pixel CMOS sensors. Still further, the thermally tunable focusing Fresnel zone plate or the ultra-compact spectrometer  20  of the present invention can both be used as a temperature sensor due to their thermal response. In this application, temperature stabilization may be used to establish a consistent baseline temperature and then changes to this baseline are measured by external sensors. 
     Referring now to  FIGS. 6-7 , an example of the above can be shown. As shown, broadband light can be directed onto the thermally tunable spectrometer  26  in array  28  for spectrometer  20 . The spectrometer can be set at temperature T. At temperature T, λ=580 nm light  36  can be tightly focused into a spot  38  that is within a single pixel  26  in the array  28 . The spectrometer temperature, the light beam spot size, the light spot intensity and the corresponding wavelength can be recorded. 
     The temperature can then be increased to T+λT. Once this occurs, the Fresnel zone plate  22  can function to refocus light so that the spot of light now covers several pixels. The spectrometer temperature, the spot intensity and beam spot size can be recorded, and provided as an input to processor  34 , along with the temperature, the focal length and the materials of construction, dimensions and thermal expansion properties of the Fresnel zone plate  22 . If light intensity on pixel  26  is below a certain level, light at the particular temperature T+ΔT can be deemed to be not present. 
     Next, the temperature T can be increased by a second increment of λT to T+2ΔT. The second increase of temperature can result in light being tightly focused (again) onto a single pixel  28 , but at a different wavelength. The focused light wavelength in  FIG. 7  can be λ=632 nm. The updated spectrometer temperature, the light beam spot size, the spot intensity and the corresponding wavelength can be recorded, and the broadband light spectrum (output wavelength λ) as a function of intensity can be plotted out to yield an output spectroscopy. 
     Referring now to  FIG. 8 , a block diagram  60  is shown, which can be used to illustrate steps that can be taken the practice the methods of the present invention according to several embodiments. As shown method  60  can include the initial step  62  of providing a pixel  26  (or a pixel  26  in a pixel array  28 ) and affording a Fresnel zone plate  22  having known dimensions and known thermal expansion coefficient α, as shown by block  64 . The methods  60  can further include the step  66  of placing the pixel  28  and the Fresnel zone plate apart from each other at a distance equal to focal length f. As shown by  FIG. 8 , the methods can further include the step of selectively heating the Fresnel zone plate  22 . In some embodiments, the heating can be accomplished in increments of ΔT. 
     The heating step can cause thermal expansion of the Fresnel zone plate  22 , as described above. The thermal expansion due to heating can further cause refocusing of radiation at different wavelengths λ i  according to the temperature of the Fresnel zone plate  22 , which will cause the pixel to register (or not) the presence of light (or not), or the degree of intensify of light at the focal point at pixel  26 , which can be indicative of the presence of a particular wavelength in the radiation  32 . 
     The use of the terms “a” and “an” and “the” and similar references in the context of describing the invention (especially in the context of the following claims) is to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. The terms “comprising”, “having”, “including” and “containing” are to be construed as open-ended terms (i.e., meaning “including, but not limited to,”) unless otherwise noted. Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., “such as”) provided herein, is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the invention. 
     Preferred embodiments of this invention are described herein, including the best mode known to the inventors for carrying out the invention. Variations of those preferred embodiments may become apparent to those of ordinary skill in the art upon reading the foregoing description. The inventors expect skilled artisans to employ such variations as appropriate, and the inventors intend for the invention to be practiced otherwise than as specifically described herein. Accordingly, this invention includes all modifications and equivalents of the subject matter recited in the claims appended hereto as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the invention unless otherwise indicated herein or otherwise clearly contradicted by context.