Discrete wavelength spectrometer

A diffraction grating, diffraction structure or Fresnel zone device is formed on a first substrate for diffracting light components of different wavelengths. An array of detectors is formed on a second substrate for detecting different wavelength components diffracted where the second substrate is spaced apart from the grating, structure or device to form a spectrometer. Spectrometers sensitive to the particular spectral lines may be used for detecting the presence of substances. The spectral resolution at such spectral lines may be increased relative to other regions to enhance the sensitivity of detection. This is done by inverse Fourier transform of the desired discrete spectrum to obtain a desired transmission function and by half-toning the aperture function.

BACKGROUND OF THE INVENTION 
This invention relates in general to spectrometers, and in particular, to a 
discrete wavelength spectrometer. 
Conventional spectrometers operate by using a grating which diffracts the 
incident wideband light beam into a continuum of wavelengths. The higher 
the wavelength, the larger the angle of diffraction. By rotating the 
grating, the diffracted beam is scanned across a photodetector and the 
intensity at each wavelength is detected. Conventional spectrometers are 
large in size and expensive to build because of the many mechanical 
components necessary for the accurate beam scan. 
There has been recently increased research activity directed towards 
developing spectrometers for sensing applications and for wavelength 
division multiplexing (WDM) in optical communication. However, a simple 
low-cost solution with an integrated detector still lacks. Goldman et al. 
proposed a planar wavelength with a diffraction grating that can be used 
for coupling light between a chemical medium and a detector array. See 
"Miniaturized Spectrometer Employing Waveguides and Grating Couplers for 
Chemical Analysis," by Goldman et al., Applied Optics, Vol. 29, No. 31, 
pp. 4583-4589, Nov. 1, 1990. However, the authors did not address 
integrating the detector with the waveguide. Holm-Kennedy et al. described 
a distributed wavelength filter based on a Fabry-Perot cavity with varying 
thickness. See "A Novel Monolithic, Chip-Integrated, Color Spectrometer: 
The Distributed Wavelength Filter Component," by Holm-Kennedy et al., 
Current Developments in Optical Design and Optical Engineering, SPIE Vol. 
1527, pp. 322-331, 1991. Integration of the filter with a detector was, 
however, not discussed by the authors. Cremer et al. presented a system 
for WDM fabricated in InGaAsP/InGaAs/InP. See "Grating Spectrograph 
Integrated with Photodiode Array in InGaAsP/InGaAs/Inp," by Cremer et al, 
IEEE Photonics Technology Letters, Vol. 4, No. 1, pp. 108-110, 1992. The 
waveguides used to channel the light from a grating to a detector array 
limit the efficient use of the spectrometer to the infrared. Furthermore, 
the fabrication process is complex, resulting in increased manufacturing 
costs. A recently awarded patent to Dunn and Langley, U.S. Pat. No. 
5,020,910, describes forming a diffraction grating directly over a 
photodetector. The grating acts as a light filter where only wavelengths 
shorter than the grating pitch are allowed through the grating and thus 
are detected. However, this device suffers from two shortcomings. First, 
the output of the detector measures the sum of the intensities at all 
wavelengths shorter than the grating pitch; electronic decomposition of 
the signal using external circuitry is necessary to obtain a useful 
spectrum of the incident illumination. Second, in order to obtain a 
spectral resolution that matches that of existing spectrometers, the 
required degree of accuracy on the grating pitch will have to be much 
smaller than the wavelength of the illumination. Such an accuracy cannot 
be achieved using existing lithographic tools. Yet another approach is 
proposed by Smith III et al. in U.S. Pat. No. 5,037,201, where a number of 
photodetectors are formed on a transparent substrate which resolves a 
polychromatic image by means of diffraction. Since the photodetectors are 
formed directly on the transparent substrate, the spectrometer proposed by 
Smith III et al. is much more limited in the choice of detectors and 
involves complex and costly fabrication processes. 
None of the above-described approaches is entirely satisfactory. It is 
therefore desirable to provide an improved discrete wavelength 
spectrometer where the above-described difficulties are alleviated. 
SUMMARY OF THE INVENTION 
One aspect of the invention is directed towards a discrete wavelength 
spectrometer comprising a diffraction grating, a semiconductor first 
substrate spaced apart from the grating, and an array of detectors on the 
first substrate at such locations that each detector is located to detect 
light diffracted by the grating at a different predetermined diffraction 
angle corresponding to a particular sub-interval of wavelengths of the 
diffracted light. 
Another aspect of the invention is directed towards a method for making a 
discrete wavelength spectrometer comprising the following steps. At least 
one diffraction grating, diffraction structure or Fresnel zone device is 
produced on a first substrate for diffracting light components of 
different sub-intervals of wavelength at different angles. An array of 
detectors is fabricated on a second substrate at such locations that each 
detector is located to detect light diffracted by the at least one 
diffraction grating, diffraction structure or Fresnel zone device and to 
detect a particular sub-interval of wavelengths of the diffracted light 
when the array is at a particular spacing from the diffraction grating, 
diffraction structure or Fresnel zone device. The position of the array is 
fixed so that the array is at said spacing to the diffraction grating, 
diffraction structure or Fresnel zone device. 
Another aspect of the invention is directed towards a discrete wavelength 
spectrometer comprising a first member having a plurality of Fresnel zone 
devices thereon, each of said devices focusing light of a different 
sub-interval of wavelengths onto a focal region on a common image plane, 
and a second member having an array of detectors thereon, each of the 
detectors located substantially in said image plane and at a focal region 
of a corresponding Fresnel zone device. 
Yet another aspect of the invention is directed towards an apparatus for 
detecting from a sample the presence of a substance having a 
characteristic optical spectrum, comprising means for generating light 
having components characteristic of the optical spectrum of the material 
in the sample, at least one diffraction structure for diffracting said 
components at predetermined diffraction angles, and a semiconductor first 
substrate spaced apart from the diffraction structure. The apparatus 
further includes an array of detectors on said first substrate. The 
diffraction structure and the detectors are such that each detector is 
located to detect one of the components in order to detect the presence of 
the substance. 
One more aspect of the invention is directed towards a spectrometer 
comprising a diffraction structure for diffracting light components at 
different angles, wherein different diffraction angles are indicative of 
different sub-intervals of wavelength of diffraction components, wherein 
the transmission function of the diffraction structure is such that 
spectral resolution at at least one sub-interval of wavelength for a 
component is higher than the spectral resolution of some other 
sub-intervals. The spectrometer further includes an array of detectors to 
detect the components at said sub-intervals. 
Yet another aspect of the invention is directed towards a method for making 
a discrete wavelength spectrometer for detecting a substance. The method 
comprises producing a diffraction structure for diffracting light, so that 
light components within different sub-intervals of wavelengths of a light 
spectrum that characterize said substance are directed at predetermined 
diffraction angles. The method further comprises fabricating an array of 
detectors on a substrate at selected locations to detect said light 
components at said predetermined diffraction angles, and fixing the 
position of the substrate and array relative to the diffraction structure.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
FIG. 1 is a cross-sectional view of a portion of a discrete wavelength 
spectrometer to illustrate one aspect of the invention. The spectrometer 
of FIG. 1 eliminates the need for moving objects by dividing the spectrum 
into a number of wavelength sub-intervals and dedicating a single detector 
for each of these subintervals. This effectively quantizes the continuum 
of the spectrum into useful wavelength bands whose widths depend on the 
number of available detectors. This quantization scheme is similar to the 
principle of operation of an electronic analog-to-digital converter. The 
structure of the spectrometer utilizes a single lithographically patterned 
diffraction grating separated from a detector array by a small distance 
such as 2 or 3 millimeters. As shown in FIG. 1, the incident light beam 18 
is diffracted by a grating 22 which "breaks up" the beam into its 
components with wavelengths .lambda..sub.1, .lambda..sub.2, 
.lambda..sub.3, .lambda..sub.4. Each wavelength is diffracted at a 
specific angle dependent only on the wavelength itself and the pitch of 
the grating. The component of wavelength .lambda..sub.1 passes through 
grating 22 to reach detector 31 of detector array 24. Component with 
wavelength .lambda..sub.2 is diffracted by a small angle towards detectors 
32, etc. As shown in FIG. 1, the components with larger wavelengths are 
diffracted at larger angles towards detectors that are further laterally 
displaced from the path of beam 18. By properly positioning a detector 
under the grating to match the corresponding diffraction angle of a 
particular wavelength component, the intensity of the beam at that 
particular wavelength is measured. 
The spectral resolution of the spectrometer 20 is determined only by the 
angle subtended by the detector with respect to the incident light beam, 
enhanced by the width of the detector, W. Given a grating-to-detector 
spacing D and a grating pitch p, a first-order estimate of the spectral 
resolution d.lambda. is given by: 
EQU d.lambda..apprxeq.W*p/D 
A device configuration capable of achieving a spectral resolution of 1 nm 
(comparable to that delivered by conventional spectrometers) would utilize 
a detector 5 microns wide, a 0.5 micron pitch diffraction grating at a 
grating-to-detector spacing of 2.5 millimeters. These design values are 
easily achievable using integrated circuit fabrication and micromachining 
techniques. Even though the above dimensions are preferred, a wider range 
of dimensions are possible. For example, the pitch of the diffraction 
grating may take on any value less than about 5 microns and the width of 
detectors may take on any value less than about 30 microns. The spacing D 
may take on values less than about 10 millimeters. All such possible 
values are within the scope of the invention. 
As shown in FIG. 1, spectrometer 20 includes a diffraction grating 22, an 
array of detectors 24 on a substrate 26, where the detectors are located 
at such locations on the substrate that each detector is located to detect 
light diffracted by the grating at a different predetermined diffraction 
angle corresponding to a particular sub-interval of wavelengths of 
diffracted light. Substrate 26 is spaced apart from the grating 22 and 
need not be transparent. Since the array of detectors are fabricated on 
the substrate which does not need to be transparent, a wide variety of 
detectors is possible. Where substrate 26 includes a single crystal 
silicon material, conventional semiconductor manufacturing techniques may 
be employed, thereby greatly simplifying the manufacturing process of the 
spectrometer and reducing the overall cost. 
In the preferred embodiments, spectrometer 20 includes a transparent second 
substrate 28 supporting the grating 22, where the second substrate is in 
contact with the first substrate 26, so that the spacing D between the 
detector array and the diffraction grating can be set by the thickness of 
the substrate layer 28. 
Spectrometer 20 of FIG. 1 may be fabricated as follows. Grating 22 is first 
produced on substrate 28. The array 24 of detectors is then fabricated on 
substrate 26 to detect a particular sub-interval of wavelengths of the 
diffracted light when the array is at a particular spacing from the 
diffraction grating. Then the position of the array is fixed so that it is 
at said spacing to the grating. This can be done conveniently by 
anodically bonding the two substrates 26, 28 together. Alternatively, the 
two substrates may be bonded together by transparent optical glue. Both 
techniques are well known. Electrical connections to the detector array 
may be made by bonding wires to bond pads on the silicon substrate 26 or 
by patterns of conductive traces on the surface of or in substrate 26. 
The array 24 of detectors can be of any type such as IR detector, pin 
diode, charge couple device, etc. Preferably, the detectors are small 
enough in area to fit an array of such detectors under the grating. 
As an alternative method of fabrication, the detector array 24 is first 
fabricated on substrate 26 and a fixed sacrificial layer is then deposited 
on or bonded to substrate 26 and the diffraction grating 22 is patterned 
on top of the sacrificial layer. The sacrificial layer is then removed at 
the end to result in a free-standing diffraction grating over the detector 
array where the grating is held together by a frame 28' as shown in dotted 
line in FIG. 1. 
Substrate 28 may be made of a transparent material such as glass or quartz. 
If substrate 28 is not transparent, then portions of substrate 28 along 
the paths of the light beams of components .lambda..sub.1, .lambda..sub.2, 
. . . , are removed by processes such as etching to permit the diffracted 
components of beam 18 to pass from the grating 22 to the array 24 of 
detectors. This step is performed before the two substrates 26 and 28 are 
attached together. 
FIG. 2 is a block diagram of a circuit for use with spectrometers such as 
that of FIG. 1 to provide an output. As shown in FIG. 2, the output of 
each of the detectors in array 24 is amplified by an amplifier 36 and the 
amplified output provided to a multiplexer 38. One of the amplified 
outputs is selected as the output 40 of the multiplexer in accordance with 
an address provided to the multiplexer along input 42. 
FIG. 3 is a cross-sectional view of a discrete wavelength spectrometer 
using a Fresnel zone plate to illustrate another aspect of the invention. 
Fresnel zone plates are described, for example, by Hecht et al. on pages 
375-376 of Optics, Addison-Wesley Publishing Company Reading, Mass. 1979. 
Spectrometer 50 of FIG. 3 includes a substrate 28 or a frame 28' 
supporting a first member having a plurality of Fresnel zone devices 
thereon, such as a plurality of Fresnel zone plates or Fresnel zone lenses 
60. Each of the Fresnel zone plates or lenses focuses light of different 
sub-interval of wavelengths onto a focal region onto an image plane 54. 
The section of the spectrometer 50 shown in FIG. 3 illustrates only one of 
the Fresnel zone devices and only one detector, it being understood that 
other sections of the spectrometer 50 would include at least one other 
Fresnel device and detector arrangement similar to that shown in FIG. 3. 
As known to those skilled in the art, the Fresnel zone plate or lens will 
focus different wavelength components of beam 18 to different depths as 
illustrated in FIG. 3. Thus, components with longer wavelengths such as 
wavelength .lambda..sub.3 will be diffracted at sharper angles and 
therefore be focused at shallower depths compared to other wavelength 
components such as .lambda..sub.1, or .lambda..sub.2. As shown in FIG. 3, 
the Fresnel zone plate 60 in the member 52 is of such design and pattern 
that it focuses components of wavelength .lambda..sub.1 of beam 18 onto 
the image plane 54. Detector 62 is located in the focal region of device 
60 to receive and detect the .lambda..sub.1 components. Since other 
wavelength components are not focused onto detector 62, they may have 
negligible effect on the detector. While detectors of array 24 of FIG. 1 
are in the shape of elongated strips, detector 62 may have circular or 
other shapes that are not elongated. Spectrometer 50 includes at least one 
more Fresnel zone device such as a Fresnel zone plate or lens that is 
patterned to focus components of a different wavelength, such as 
.lambda..sub.2 or .lambda..sub.3, onto image plane 54 where another 
detector similar to detector 62 will be located to receive and detect such 
components. With such patterns of Fresnel zone devices, it is then 
possible to locate all the detectors for detecting different wavelength 
components on a common image plane 54. 
Spectrometer 50 can therefore be used to detect different wavelength 
components within certain selected sub-intervals of a spectrum by 
selecting those Fresnel zone devices that will focus wavelength components 
within such selected sub-intervals onto common image plane 54. While in 
the preferred embodiment image plane 54 is parallel to the plane of member 
52, it will be understood that this is not necessary; such and all other 
variations are within the scope of the invention. The process for 
fabricating spectrometer 50 is similar to that of spectrometer 20 
described above. 
The spectrometers of this application described above may be used 
advantageously to detect the presence of particular substances, especially 
where the substance has distinct and specific spectral lines. FIG. 4 
illustrates the typical spectrum of a gas. As shown in FIG. 4, it is 
evident that the typical spectrum of a gas exhibits several sharp peaks, 
so that if high intensity components of wavelengths corresponding to such 
sharp peaks of the gas spectrum are detected from light generated from or 
emitted by a substance, the presence of the gas in such substance is 
detected. For example, the spectral lines of hydrogen are at 656.2 nm, 
486.1 nm, 479.7 nm, 410.1 nm etc. The detection of substances can be 
extended to beyond the emission spectrum of substances to the spectrum of 
light transmitted through (a reverse form of absorption spectrum) or 
reflected by substances as well. 
FIG. 5 is a schematic view of a system using the spectrometer of this 
application for detecting substances in samples to illustrate the 
preferred embodiment of the invention. As shown in FIG. 5, light 
containing all the wavelength components characteristic of the optical 
spectrum of a substance (such as white light) and generated by a light 
source 100 is passed through a sample 102 as beam A to a spectrometer 104. 
If the light from source 100 stimulates light emission from sample 102, 
then the light emitted by sample 102 is supplied to spectrometer 104 for 
detection of the substance. Alternatively, if the substance in sample 102 
is distinguished by the light absorbed by it, then the light transmitted 
through sample 102 originating from source 100 is sent to spectrometer 104 
for detection. In either case, spectrometer 104 is constructed for 
detecting particular substances by selecting either a grating 22 or 
Fresnel zone devices 52 designed to detect wavelength components within 
certain selected sub-intervals of the spectrum that characterize the 
substance. Then the detection of high intensity wavelength components in 
those sub-intervals would indicate the presence of the substance. Where 
the substance in the sample is characterized by light reflected by it, an 
alternative to the above-described system is to detect the reflected light 
beam B from sample 102' instead of beam A and the sub-intervals of 
detection for spectrometer 104 would then be selected as a characteristic 
of the reflection spectrum of the sample 102'. A similar scheme may be 
used for substance detection by detecting refracted light. 
Re-Allocation of Spectral Resolution 
The separation of the incident illumination into its wavelength components 
can be also understood using basic Fourier optics. In its simplest form, 
given a transmission function T, where T=1 is for total transmission 
(transparent) and T=0 is for total opacity, the far field diffraction 
pattern (also known as Fraunhofer diffraction) at the image plane is 
proportional to the Fourier transform of T. For the simple case of an 
ideal grating which is an infinite square periodic transmission function, 
its Fourier transform is a sequence of impulses (or delta functions) 
uniformly separated with the separation set by the periodicity of the 
grating and the wavelength of the illuminating light. For single 
wavelength illumination, the grating generates diffraction orders located 
at each of the impulses described above. The first is called 1st order, 
the second 2nd order, . . . , etc. When white light is used, each 
wavelength component has its own set of diffraction orders separated from 
other wavelength components by the ratio of the wavelengths (for a given 
grating periodicity). Only the 1st order is of interest to us in this 
device. The overall spectral resolution using the grating is uniform at 
all wavelengths and is set by the number of detectors in the detector 
array, the grating pitch and the separation between the diffraction 
structure 22 and the detector array 24. 
FIG. 6A is a spectrometer having a transmission function useful for 
illustrating the concept of re-allocation of spectral resolution. Where 
the transmission function is a periodic grating, the wavelengths are 
uniformly spaced with a separation determined by the pitch (periodicity) 
of the periodic grating. The separation determines the spectral resolution 
of the device according to the formula referenced above for d.lambda.. 
FIG. 6B illustrates a spectrum obtained using a periodic grating. As shown 
in FIG. 6B, at the peak of the spectrum near wavelength .lambda..sub.3, 
there is only one detection point by one detector for detecting the peak, 
whereas the remaining five detection points by five detectors detect 
wavelengths that are away from the spectral line indicated by the peak. 
In some particular applications, a uniform spectral resolution is not of 
interest. Rather, it is desirable to expand the spectral resolution in 
some areas and compress it in others. This is particularly the case in the 
detection of gases or chemicals which have spectral lines as specific 
wavelengths in the spectrum and little energy in between. In such event, 
it will be desirable to expand the spectral resolution in the neighborhood 
of the spectral lines of the gas or chemical and compress it in the 
remaining areas. In the context of FIG. 6B, for example, it will be 
desirable to increase the spectral resolution and the number of points of 
detection at and close to the peak and reduce the number of points of 
detection away from the peak. Such desirable transmission function is 
illustrated in FIG. 6C. As shown in FIG. 6C, the optimized transmission 
function permits three detection points at and close to the peak and only 
two detection points away from the peak. The overall number of detectors 
remains unchanged. 
It is of course possible to increase the density of detection points by 
increasing the density of detectors on the image plane where the 
diffracted wavelength components at the spectral lines of interest would 
strike and decrease the density of detectors at other areas. From the 
manufacturing point of view, instead of increasing detector density at 
certain locations on a substrate, it is much easier and less expensive to 
manufacture detector arrays that are uniformly spaced but where the 
diffraction angles of the wavelength components at the spectral lines of 
interest resulting from the transmission function are changed to 
redistribute such components to where the detectors are in order to 
increase detection points at the wavelengths of interest. This is 
equivalent to steering particular wavelengths to preset detector 
locations. The problem posed is therefore to find a transmission function 
in order to obtain the required spectral resolution at the image plane 
where the detectors are uniformly spaced in the image plane. 
The above described problem is known as the inverse problem and its 
solution lies in a sequence of computational steps described next. First, 
the desired diffracted field distribution, that is the distribution of the 
diffracted wavelength components across the image plane is defined by the 
user. That includes defining the wavelength sub-intervals where the 
resolution is higher than that in other sub-intervals. Next, an aperture 
function is computed from the desired diffracted field distribution. This 
is done by performing an inverse Fourier transform on the desired 
diffracted field distribution as clearly described by Hecht et al. on 
pages 347, 411-414 of Optics, Addison-Wesley Publishing Company Reading, 
Mass. 1979. The resulting aperture function will be a complex function, 
that is, it will have a magnitude and a phase. 
FIG. 7A is the graphical illustration of an aperture function of a uniform 
grating. FIG. 7B illustrates a spectrometer having a uniform grating and 
FIG. 7C illustrates the diffraction spectrum of the spectrometer of FIG. 
7B. As explained above in referenced to FIG. 6B, again the detection 
points in FIG. 7C for uniform grating are not concentrated at the spectral 
lines of interest but are distributed uniformly across the spectrum and 
the spectral resolution is uniform across the spectrum and is 
approximately equal to the spectrum range divided by the number of 
detectors. 
FIG. 8A illustrates an optimized complex aperture function for increasing 
the spectral resolution at the spectral lines of interest and relative to 
the spectral resolution at other areas of the spectrum. FIG. 8B is a 
cross-sectional view of a spectrometer having the aperture function of 
FIG. 8A and FIG. 8C illustrates the diffraction spectrum of the 
spectrometer of FIG. 8B with re-allocated spectral resolution at the 
spectral lines of interest. As shown in FIG. 8C, the spectral resolution 
d.lambda..sub.1 near the spectral lines of interest is finer than 
d.lambda..sub.2, the spectral resolution in the regions outside of the 
spectral lines. Even though the total number of detectors illustrates in 
FIGS. 7C, 8C are the same, more detectors are allocated for the spectral 
lines of interest in FIG. 8C than in FIG. 7C. 
As a practical matter, it may be necessary to find a physical 
implementation of the complex aperture function A shown in FIG. 8A rather 
than the continuous function shown in the figure. This is illustrated in 
FIGS. 9A, 9B. A will have a magnitude and a phase term. The aperture 
function A obtained using the above-described inverse Fourier transform 
process will almost always be a complex solution. In half-toning, the 
magnitude can only be set to 0 (opaque) or 1 (transparent) in most 
manufacturing processes. The phase can be adjusted by angles between 
0.degree. and 180.degree. easily; to adjust the phase by 180.degree., the 
transparent substrate is etched by half of the wavelength. Similarly, a 
90.degree. phase shift may be implemented by etching this transparent 
substrate by one-quarter of the wavelength and so on for other different 
degrees of phase shift. As a practical matter, however, it may be adequate 
to implement only the 0.degree., 90.degree. and 180.degree. phase shift, 
thereby etching the transparent substrate by half and one-quarter of the 
wavelength of the component of the light involved in a process known as 
dithering. 
The dithering or half-toning process is illustrated in FIG. 9A. Thus, at 
locations where the aperture function A has the magnitude 0, the 
transparent substrate 28 is covered by an opaque layer 120. Where the 
magnitude of the aperture function A is a 1 such as at regions 122, 124, 
transparent substrate 28 is not covered by the opaque layer at all to 
allow light transmission therethrough. Region 122 of transparent substrate 
has been etched downwards by a distance equal to one-quarter of the 
wavelength and region 124 has been etched downwards by a distance of half 
of the wavelength of the component of interest, illustrating how the phase 
of the light passing through can be altered by a transmission function 
that approximates the phase term of an aperture function. 
FIG. 9B illustrates a diffraction structure having a transmission function 
whose amplitude approximates that of the aperture function A desired, 
using half-toning, a process well-known to those in the printing art. 
Thus, where the amplitude of the aperture function is 0, the transparent 
substrate 28 is covered entirely by an opaque layer 120. Where the 
amplitude of the aperture function is a half, the opaque pixel dots of 
opaque layer 130 in such area would occupy and cover only half of the 
surface area of the transparent layer in such region. Where the amplitude 
of the aperture function is two-thirds, then the dots of opaque layer 140 
covers only one-third of the total surface area of the transparent layer 
in this region and so on. Individual opaque dot pixels are much smaller in 
size compared to the total area that is being dithered. The amplitude of 
the transmission function resulting from the half-toning process is given 
by the ratio of the area of the transparent region to the area of the 
opaque region. 
FIG. 10 is a block diagram of a system for making a spectrometer with a 
desired-re-allocated spectral resolution. First, the desired field 
distribution in the image plane is discretized by a discretizing map 200. 
This map can be implemented simply by setting to zero the amplitudes of 
the field in regions with no measurements of interest. An inverse fast 
Fourier transform process is then performed in block 202 to obtain the 
aperture function which as discussed above is usually a complex function 
having an amplitude term and a phase term. The half-toning process is 
performed in block 204 on the complex aperture function in the manner 
explained above in reference to FIGS. 9A, 9B and the transmission function 
resulting from the half-toning process is applied to lithographic 
equipment 206 for making masks. One mask is necessary for determining 
which areas of an opaque layer on top of a transparent layer should be 
etched away to allow light transmission therethrough; such mask is derived 
from the amplitude of the transmission function. One would first start out 
with a transparent substrate having an opaque layer on top attached 
thereto. The transparent substrate underneath is exposed in areas where 
portions of the opaque layer have been etched away as determined by the 
mask which is a digital approximation of the amplitude of the aperture 
function. Then the mask for etching the transparent substrate by 
one-quarter of the wavelength is applied and the transparent substrate 
etched to such depth. Then the mask for etching the transparent substrate 
to half of the wavelength is applied and the substrate so etched. 
The algorithm and the approximating imaging system model for the 
above-described phase shifting masks are described in detail in the 
article, "Phase-Shifting Masks: Automated Design and Mask Requirements," 
by Pati et al., Proceedings, SPIE Vol. 2197, pp. 314-327, March 1994. 
Multi-phase-shifting and half-tone phase-shifting masks actually made are 
described in the article, "Imaging Characteristics of Multi-Phase-Shifting 
and Halftone Phase-Shifting Masks," by Terasawa et al., pp. 2991-2997, 
November 1991. 
While the invention has been described above by reference to various 
embodiments, it will be understood that different changes and 
modifications may be made without departing from the scope of the 
invention which is to be limited only by the claims.