Abstract:
The present invention relates to an optical interferometric apparatus and method for measuring acceleration, pressure, and pressure of fluids during flow using micro-opto-electro-mechanical-systems (MOEMS). The high-sensitivity and high-resolution apparatus includes a movable mass, a stationary mass, a light source, and a photo detector. The light source emits a beam which is converted into two beam portions after impinging onto the movable and stationary masses. Interference between the beam portions are used to measure acceleration or pressure. The MOEMS structure may be integrated with a photo detector or planar waveguide. Differential amplification can be realized by employing two similar detecting structures.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
   This application is entitled to the benefit of Provisional Patent Application Ser. No. 60/648,423, filed Feb. 1, 2005 and Ser. No. 60/766,579, filed Jan. 30, 2006. 

   FEDERALLY SPONSORED RESEARCH 
   Not applicable 
   SEQUENCE LISTING OR PROGRAM 
   Not applicable 
   BACKGROUND 
   1. Field of Invention 
   This invention relates to optical interferometric sensors, particularly to interferometric MOEMS accelerometers and pressure sensors. 
   2. Description of Prior Art 
   High-sensitivity and high-resolution accelerometers have applications in seismology and navigation. They are also used in monitoring systems of structure condition. In the applications, low cost and small size of an accelerometer are often required besides sensitivity and resolution. Among currently available methods for acceleration detection, e.g. capacitative, piezoresistive, piezoelectric, tunneling, and optical interferometric schemes, the optical interferometric scheme has an advantage over the others in terms of specification and cost when it is combined with micro-electro-mechanical-systems (MEMS). When MEMS is blended with optics, it is often call optical MEMS or micro-opto-electro-mechanical-systems (MOEMS). 
   In U.S. Pat. No. 6,473,187 to Manalis, a MOEMS accelerometer is disclosed in which an interferometer consists of micromachined interdigital fingers and one set of the fingers moves when it is subject to acceleration. In U.S. Pat. No. 6,763,718 to Waters et al., another type of MOEMS accelerometer is taught where an adjustable Fabry-Perot interferometer is fabricated and used for the measurement. In the prior art, however, the interdigital fingers or Fabry-Perot cavity mean a complex structure, which adds to manufacturing difficulties and restricts reduction of size. 
   Accordingly, there is a need for a high-sensitivity and high-resolution MOEMS accelerometer which is smaller in size and easier to make compared to the present ones. 
   A compact high-sensitivity pressure sensor is often made by attaching or forming a Fabry-Perot interferometer at the end of an optical fiber. Again, the Fabry-Perot cavity, having two well-aligned parallel reflectors, is difficult to fabricate. In addition, when one reflector moves due to change of pressure, characteristics of the interferometer are prone to deteriorate. 
   Therefore, there exists a need for a compact pressure sensor which is relatively easier to fabricate and has high-sensitivity. 
   OBJECTS AND ADVANTAGES 
   Accordingly, several main objects and advantages of the present invention are: 
   a) to provide an improved high-sensitivity and high-resolution MOEMS accelerometer; 
   b) to provide such an accelerometer which has a relatively simple and small structure and is relatively easy to manufacture; 
   c) to provide such an accelerometer which uses a light source, a stationary mass, a movable mass, and a photo detector to achieve high-sensitivity and high-resolution and a compact structure; 
   d) to provide an improved high-sensitivity MOEMS pressure sensor; 
   e) to provide such a sensor which has a relatively simple and small structure and is relatively easy to manufacture; and 
   f) to provide such a sensor which employs a light source, a stationary mass, a movable membrane, and a photo detector to achieve high-sensitivity and a compact structure. 
   Further objects and advantages will become apparent from a consideration of the drawings and ensuing description. 
   SUMMARY 
   An interferometric MOEMS accelerometer contains a light source, a detector, a stationary mass, and a movable mass. The light source emits a beam which impinges onto the masses simultaneously. After interacting with the masses, the beam is converted into two beam portions having a phase difference. Since position of the movable mass is subject to acceleration, the phase difference is used to obtain acceleration through analyzing interference between the beam portions. Similar principles also apply to a MOEMS pressure sensor, where the movable mass is replaced by a membrane. 
   ABBREVIATIONS 
   MEMS Micro-electro-mechanical-systems 
   MOEMS Micro-opto-electro-mechanical-systems 

   
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       FIGS. 1-A  and  1 -B are schematic cross-sectional views of a prior-art optical interferometric surface profiler. 
       FIGS. 2 ,  3 -A,  3 -B, and  4  to  9  are schematic cross-sectional views showing embodiments of several reflection-type MOEMS accelerometers. 
       FIG. 10  is a schematic cross-sectional view of an embodiment of a reflection-type MOEMS pressure sensor. 
       FIGS. 11 ,  12 -A,  12 -B are schematic cross-sectional views and a top view showing embodiments of transmission-type MOEMS accelerometers. 
       FIG. 13  is a schematic cross-sectional view showing an embodiment of a MOEMS accelerometer integrated with a photo detector. 
       FIG. 14  is a schematic cross-sectional view of an embodiment of a transmission-type MOEMS pressure sensor. 
       FIGS. 15-A ,  15 -B, and  16 -A to  16 -C are schematic cross-sectional views, diagrams, and a top view showing embodiments of transmission-type MOEMS accelerometers which have capability of differential amplification. 
       FIGS. 17-A ,  17 -B, and  18  to  21  are schematic top and cross-sectional views showing embodiments of MOEMS accelerometers employing planar waveguides to transmit a beam. 
       FIG. 22  is a schematic cross-sectional view of a MOEMS pressure sensor for fluids. 
     
       
         
               
             
               
               
               
               
             
           
               
                   
               
               
                 REFERENCE NUMERALS IN DRAWINGS 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                  12 
                 collimated beam 
                  14 
                 modulator element 
               
               
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                 modulator element 
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                 spatial phase modulator 
               
               
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                 beam portion 
                  20 
                 beam portion 
               
               
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                 sample 
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                 sample 
               
               
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                 sample surface 
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                 fixed mass 
               
               
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                 movable mass 
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                 lens system 
               
               
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                 sample surface 
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                 sample surface 
               
               
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                 cantilever 
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                 fixed end 
               
               
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                 light source 
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                 photo detector 
               
               
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                 lens system 
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                 photo detector 
               
               
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                 lens system 
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                 beam splitter 
               
               
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                 electrode surface 
                  58 
                 electrode surface 
               
               
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                 movable mass 
                  61 
                 beam 
               
               
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                 movable mass 
                  64 
                 phase tuning device 
               
               
                  66 
                 lens system 
                  68 
                 optical fiber 
               
               
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                 fiber optic coupler 
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                 gap 
               
               
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                 optical fiber 
                  74 
                 optical fiber 
               
               
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                 fixed mass 
                  76 
                 substrate 
               
               
                  80 
                 light source 
                  82 
                 photo detector 
               
               
                  88 
                 mass surface 
                  90 
                 mass surface 
               
               
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                 mass surface 
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                 substrate 
               
               
                  94 
                 mass surface 
                  96 
                 membrane 
               
               
                  97 
                 movable mass 
                  98 
                 cavity 
               
               
                 100 
                 fixed end 
                 102 
                 cantilever 
               
               
                 104 
                 fixed mass 
                 106 
                 movable mass 
               
               
                 108 
                 waveguide channel 
                 110 
                 beam splitter 
               
               
                 112 
                 waveguide channel 
                 114 
                 waveguide channel 
               
               
                 116 
                 detector 
                 118 
                 light source 
               
               
                 120 
                 waveguide end 
                 126 
                 substrate 
               
               
                 128 
                 beam 
                 130 
                 fixed mass 
               
               
                 132 
                 fixed mass 
                 136 
                 convergent beam 
               
               
                 138 
                 detector 
                 140 
                 detector 
               
               
                 142 
                 detector 
                 143 
                 fixed mass 
               
               
                 144 
                 lens system 
                 145 
                 fixed mass 
               
               
                 146 
                 movable mass 
                 148 
                 movable mass 
               
               
                 150 
                 light source 
                 152 
                 light emitting spot 
               
               
                 154 
                 cantilever 
                 156 
                 movable mass 
               
               
                 158 
                 movable mass 
                 160 
                 cantilever 
               
               
                 161 
                 photo detector 
                 162 
                 waveguide channel 
               
               
                 163 
                 photo detector 
                 164 
                 waveguide channel 
               
               
                 165 
                 light source 
                 166 
                 waveguide channel 
               
               
                 168 
                 waveguide channel 
                 170 
                 waveguide channel 
               
               
                 171 
                 beam splitter 
                 172 
                 beam splitter 
               
               
                 173 
                 beam splitter 
                 174 
                 fixed mass 
               
               
                 176 
                 opening 
                 178 
                 membrane 
               
               
                 180 
                 cavity 
                 182 
                 blocking element 
               
               
                 184 
                 cavity 
                 186 
                 movable mass 
               
               
                 188 
                 fixed mass 
                 190 
                 cantilever 
               
               
                 191 
                 waveguide channel 
                 192 
                 waveguide channel 
               
               
                 193 
                 waveguide channel 
                 194 
                 waveguide channel 
               
               
                 196 
                 beam splitter 
                 198 
                 accelerometer substructure 
               
               
                 200 
                 accelerometer substructure 
                 201 
                 beam splitter 
               
               
                 202 
                 beam splitter 
                 203 
                 beam splitter 
               
               
                 204 
                 cantilever 
                 206 
                 movable mass 
               
               
                 208 
                 movable mass 
                 210 
                 cantilever 
               
               
                 212 
                 fixed mass 
                 222 
                 fixed mass 
               
               
                 224 
                 cavity element 
                 226 
                 movable mass 
               
               
                 228 
                 cavity 
                 230 
                 cavity element 
               
               
                 232 
                 membrane 
                 306 
                 waveguide channel 
               
               
                 308 
                 waveguide channel 
                 310 
                 fixed mass 
               
               
                 312 
                 cantilever 
                 314 
                 fixed end 
               
               
                 316 
                 movable mass 
               
               
                   
               
             
          
         
       
     
   

   DETAILED DESCRIPTION 
   FIGS.  1 -A and  1 -B—Prior-Art 
     FIGS. 1-A  and  1 -B illustrate schematic cross-sectional views of a prior-art optical interferometric surface profiler. A collimated beam  12  is transmitted through regions  14  and  16  of a spatial phase modulator  17  and is divided into beam portions  18  and  20  by wavefront division. Next the beam portions are focused onto a surface  23  of a sample  21 . The reflected beam from surface  23  is reflected by a beamsplitter  54  and focused onto a detector  50  by a focus lens  52 . 
     FIG. 1-B  shows a typical application of the device in  FIG. 1-A . Beam portions  18  and  20  are focused onto a sample  22 , where stepped surface areas  32  and  34  reflect the beam portions respectively. By tuning the phase difference between the two portions by modulator  17 , the step height can be obtained. For example, the two portions can be tuned in or out of phase. Since how much the phase is tuned is known, the step height can be calculated. 
   FIG.  2 —Embodiment of a MOEMS Accelerometer 
     FIG. 2  shows schematically a cross-sectional view of a reflection-type MOEMS accelerometer. Assume that beam portions  18  and  20  are focused onto a top surface of a fixed or stationary mass  26  and a top surface of a movable mass  28  respectively. Mass  28  is attached to a cantilever  36 , and cantilever  36  to a fixed end  38 . Mass  26  and end  38  are disposed on a substrate  76 . All items in  FIG. 2  can be made on a semiconductor wafer by mature MEMS technologies. 
   When there is acceleration along a direction perpendicular to mass  28 &#39;s top surface, cantilever  36  is bent due to inertia on mass  28 , where the displacement value is dependable on the acceleration. The bending causes a height difference change between top surfaces of masses  26  and  28 . By the same principle of the surface profiler in  FIGS. 1-A  and  1 -B, displacement of mass  28  can be obtained by tuning a spatial phase modulator. Having the displacement and the time in which the bending takes place, acceleration can be derived. 
   Since the interference method is able to achieve sub-Angstrom resolution, the accelerometer has much higher sensitivity and resolution than a MEMS accelerometer operated by electrical schemes. 
   The spatial phase modulator may use various methods to adjust phase difference between the two beam portions. Electro-optical methods employ materials like LiNbO 3  and liquid crystal. A mechanical method tunes phase delay mechanically. 
   FIGS.  3 -A and  3 -B—Embodiment of a Compact MOEMS Accelerometer 
     FIG. 3-A  shows schematically a cross-sectional view of a compact reflection-type MOEMS accelerometer. A light source  40  and a detector  42  are designed and aligned such that source  40 &#39;s light emitting spot is proximate to a light receiving area of detector  42 . Source  40  and detector  42  are placed close to fixed mass  26  and movable mass  28 . A beam from source  40  is transmitted to impinge onto the masses and is reflected back. The reflected beam contains two beam portions coming from top surfaces of masses  26  and  28  respectively. Because detector  42  is proximate to source  40 , part of the reflected beam reaches the detector which detects interference between the portions. When acceleration is zero, there is an interference value caused by the initial optical path difference. In the presence of acceleration, the optical path difference changes, and so does the interference intensity detected by detector  42 . The intensity change is used to calculate the acceleration. 
   When there is no acceleration, phase difference between the two portions may be arranged to have a value by pre-setting height difference between surfaces of masses  26  and  28 . For example, the two portions may initially have a phase difference of pi/2, which makes it possible to utilize the most linear range of the well-known interference intensity vs. phase difference curve. 
   Compared to a Fabry-Perot cavity or interdigital fingers, the structure in  FIG. 3-A  is simpler and more compact, and is easier to make. 
     FIG. 3-B  shows schematically another embodiment where a focus lens  46  is added to the set-up in  FIG. 3-A . Without the focus lens, light source  40  and detector  42  have to be placed close to the masses&#39; surfaces because the beam is divergent. Lens  46  focuses the beam onto top surfaces of masses  26  and  28 . On the other hand, part of the reflected beam is focused onto the detector. Because of the focus lens, the light source and detector may be placed away from the masses and in the meantime the signal intensity is increased. 
   To reduce feedback on light source  40 , a half wave plate may be used to rotate polarization such that a reflected beam has a polarization perpendicular to that of a beam from source  40 . 
   FIG.  4 —Embodiment of a Hybrid Accelerometer 
   As shown in a cross-sectional view in  FIG. 4 , an embodiment combines a traditional MEMS accelerometer with a MOEMS accelerometer by incorporating a capacitor structure in the schemes discussed. One electrode of the capacitor is with movable mass  28 , while the other electrode is with the substrate  76 . The capacitance is dependable upon distance between electrode surfaces  56  and  58  and it tells how much mass  28  is displaced. The capacitative method is complimentary to the interference method, since the former gives a relatively rough result, while the latter results in finer resolution. Without the former, the latter has a difficult time when the path length change due to mass  28 &#39;s displacement is larger than half of the beam&#39;s wavelength. 
   The hybrid method may be used in all embodiments here. Other electrical methods can also be used. 
   FIG.  5 —Embodiment Having Two Movable Masses 
   In a cross-sectional view in  FIG. 5 , there are two movable masses  60  and  62  along with a stationary mass  75 . Here a beam  61  is divided into three beam portions by the masses and can be viewed as two MOEMS accelerometers share one stationary mass. Masses  60  and  62  have different inertia and cantilevers. The scheme may be used to improve dynamic range of measurement. 
   FIG.  6 —Embodiment of an Improved Compact MOEMS Accelerometer 
   The embodiment in  FIG. 6  improves a MOEMS accelerometer like the one in  FIG. 3A . With reference to  FIG. 6 , a phase tuning device  64  is disposed on the surface of movable mass  28 . Device  64  makes the interference tunable. Only light travels to and from mass  28  passes through device  64 . If device  64  can&#39;t be tuned to compensate phase difference between the beam portions, at least it tells what position it is on an interference intensity vs. phase difference curve. For example, when interference intensity changes from a peak or valley, there are two possible positions due to a cosine curve. But the position can be resolved if a phase tuning is utilized, because once the phase difference is known, the curve slope can be calculated. Device  64  may also be a fixed phase element to adjust initial phase delay of the beam portion. 
   FIG.  7 —Embodiment of a MOEMS Accelerometer Employing Optical Fibers 
     FIG. 7  shows a MOEMS accelerometer which replaces the light source and detector in  FIG. 6  by a fiber optic setup. A beam from a light source  80  is coupled into an optical fiber  74 . After passing through fiber  74 , a fiber optic coupler  70 , and another optical fiber  68 , the beam is focused onto masses  26  and  28  by a lens system  66 . The reflected beam is partially coupled back into fiber  68  by lens  66  and is transmitted to a detector  82  through fibers  68  and  72 . The fiber optical coupler serves as beam splitter. Using the fiber optic arrangement, the light source and detector can be placed remotely, which is desirable in some applications. 
   FIGS.  8  and  9 —Embodiment of Improved MOEMS Accelerometer 
   In the presence of acceleration, movable mass  28  tilts, as shown schematically in a partial cross-sectional view in  FIG. 8 . The reflected beam actually contains multiple path lengths, which makes the interference result complicated. In  FIG. 8 , assuming the ambient refractive index is one, a beam portion has a dimension of d and the tilting angle is alpha, the maximum path length difference within the reflected beam portion is 2d*tan (alpha). Thus the smaller the d, the smaller the unwanted path length difference. There are two ways to minimize the effect caused by the tilt: to provide a small-size beam portion or a small-size effective surface area. In the latter case, the reflected light only comes from a small area, which equals to a small beam portion. 
   As illustrated graphically in a cross-sectional view in  FIG. 9 , a MOEMS accelerometer contains a movable mass  97  whose top surface is processed such that only a small surface area  88  contributes to reflection. Area  88  has a dimension s, much smaller than a recessed surface area  90 . Area  90  is made to deflect or scatter a beam so that it won&#39;t reach the detector. Another way is to make surface  90  out of the focus region. Stationary mass  26  may also have a small reflective area to match intensity of the interfering beam portions. 
   Area  88  makes the interference between the beam portions close to two-wave rather than multi-wave interference. As a result, data processing is simplified and measurement sensitivity is improved. 
   FIG.  10 —Embodiment of a MOEMS Pressure Sensor 
     FIG. 10  shows schematically a cross-sectional view of a reflection-type interferometric MOEMS pressure sensor. A cavity  98  on a substrate  93  is sealed by a membrane  96 . When pressure changes, membrane  96  moves up or down accordingly, so does a small surface area  94  that is disposed on the membrane. Interference between light reflected from surface  94  and  92  results in displacement of the membrane, which is used to calculate the pressure outside of cavity  98 . 
   Thanks to the similar principles, all the schemes used in the reflection-type MOEMS accelerometers can be utilized to make a MOEMS pressure sensor. 
   FIGS.  11 ,  12 -A, and  12 -B—Embodiments of MOEMS Accelarometer 
     FIG. 11  shows schematically a cross-sectional view of a transmission-type MOEMS accelerometer. A collimated beam  128  from a light source (not shown) impinges onto movable mass  28  and a stationary mass  130  simultaneously. Mass  28  is attached to cantilever  36 , which is attached to fixed end  38 . Mass  130  and end  38  are disposed on substrate  76 . 
   After beam  128  interacts with masses  28  and  130 , it becomes two beam portions, whose phase is delayed by the masses respectively. Next the two beam portions pass through substrate  76  and are focused onto a detector (the focus lens and detector not shown). The detector senses interference caused by the beam portions. The interference intensity is depended upon their phase difference. 
   When there is acceleration along a direction perpendicular to mass  28 &#39;s top surface, cantilever  36  is bent due to inertia of mass  28 . The bending makes mass  28  tilt, which in turn increases phase delay of the corresponding beam portion. Thus the bending can be detected by measuring interference intensity of the beam portions. A spatial phase modulator may also be added to adjust phase difference between the two beam portions. As a result of phase tuning, the measurement resolution is improved, since the phase difference can be tuned to any value. 
     FIG. 12-A  illustrates schematically a cross-sectional view of another transmission-type MOEMS accelerometer. This accelerometer is similar to the embodiment in  FIG. 11 , except structure of the fixed mass. In  FIG. 12-A , a stationary mass  132  has a cavity below its top surface like movable mass  28 . But mass  132  has three supported sides, as shown in a top view in  FIG. 12-B , and only one side of it, which is adjacent to a gap  71 , is suspended. The three fixed sides make mass  132  stationary. Because mass  132  and  28  share the same layer, it has merits in ease of phase delay control. 
   FIG.  13 —Embodiment of an Integrated MOEMS Accelerometer 
     FIG. 13  shows schematically a cross-sectional view of an integrated MOEMS accelerometer. The transmission-type embodiment contains fixed mass  132 , movable mass  28 , and an integrated photo detector  138  on substrate  76 . A convergent beam  136  from a light source (not shown) is focused onto detector  138  after passing through masses  132  and  28  respectively. Detector  138  senses interference intensity between the beam portions created by masses  132  and  28 . When it is subjected to acceleration, cantilever  36  is deflected and mass  28  tilts, and the interference in turn changes accordingly. Again, the measurement may be obtained by measuring an intensity value directly, or by tuning the phase difference through a spatial phase modulator and measuring a series of resulting interference intensity. 
   It is well-known that detector  138  may be a PN or PIN diode under reverse bias. The PN or PIN detector can be fabricated through conventional mature CMOS process along with the making of a MEMS device. In addition, signal amplification and control circuitry may be made on or above substrate  76  in the process. The integration of MOEMS device, photo detector, and circuitry makes the MOEMS system more robust and compact compared to the embodiment in  FIGS. 11 and 12-A , where anther focus lens, a discrete detector, and external circuitry are required. 
   FIG.  14 —Embodiments of MOEMS Pressure Sensor 
     FIG. 14  shows schematically a cross-sectional view of a transmission-type MOEMS pressure sensor. There are two cavities on a substrate  93 . A sealed cavity  180  has a membrane  178 , which moves up or down when there is a difference between the cavity and the ambient pressure. When displacement of membrane  178  occurs, a portion of incident collimated beam  128  will experience change of phase delay. On the other hand, another portion of beam  128  passes through the other cavity  184 . Cavity  184  has an opening such that it always has the ambient pressure and its membrane will not be subjected to the external force as membrane  178 . 
   Therefore, when beam  128  is focused after being transmitted through cavities  184  and  180  respectively, interference between the two portions can be used to measure the state of bending of membrane  178 . Since cavity  180 &#39;s pressure is known, ambient pressure can obtained. The two beam portions may be arranged to have a predetermined phase difference for measurement convenience, which may be done by depositing or etching a layer on the membrane of cavity  184 . If a spatial phase modulator is used to tune phase difference between the two portions, the measurement resolution can be improved. In  FIG. 14 , an element  182  is employed to block light which passes through the wall between the cavities. 
   When a photo detector and control circuitry are added like the embodiment in  FIG. 13 , the scheme here becomes an integrated MOEMS pressure sensor. 
   FIGS.  15 -A,  15 -B, and  16 -A to  16 -C—Embodiments of MOEMS Accelerometer using Differrential Amplification 
   As shown schematically in a cross-sectional view in  FIG. 15-A , another embodiment of the invention involves two accelerometers which have similar structures. The accelerometers resemble the embodiment in  FIG. 11 . They have identical movable masses  206  and  208 , identical cantilevers  204  and  210 , but use different parts of a stationary mass  212 . After collimated beam  128  passes through the accelerometers, two pairs of beam portions are generated—one by masses  206  and  212  and the other by masses  208  and  212 . Next, the beam portions are focused and one pair is focused onto one detector and the other pair onto another detector (focus lenses and detectors not shown). Thus phase difference of each pair can be measured. 
   When being subjected to acceleration, movable masses  206  and  208  tilt by the same value due to identical parts. But since the pairs experience two parts of mass  212  separately, where the parts have different thickness, one pair&#39;s phase difference is always larger than the other pair&#39;s by a fixed number. 
   Assume interference intensity I follows formula I=cos 2 (psi/2), where psi is the phase difference of the two beams. The formula is illustrated by a curve of interference intensity vs. phase difference in  FIG. 15-B . There are two middle points, marked by C and D, where the relative intensity is 0.5 at pi/2 and 3 pi/2. Around the middle point is the most linear region of the curve. 
   Arrange the masses such that points C and D represent the initial phase difference of the two pairs of beam portions. Thus initially the pairs have phase difference of pi/2 and 3pi/2 respectively. When there is acceleration, movable masses  206  and  208  tilt identically and cause the same phase change. Assume the phase change is beta. According to the interference intensity formula, intensity of one pairs becomes cos 2 (pi/4+beta/2), while the other becomes cos 2 (3 pi/4+beta/2). It is easy to show that the interference intensity is reduced by a value (sin(beta))/2 at point C for one pair, while increased by the same value at point D for the other pair. 
   Therefore, when the interference intensity of one beam portion pair at point D is subtracted by that of the other pair at point C, the result is twice the change. In other words, the two accelerometers may be utilized for differential amplification of signals and reduction of noise of the light source. 
     FIG. 16-A  schematically shows a diagram of another embodiment of MOEMS accelerometer which may use differential amplification. Two accelerometers contain detectors  140  and  142  and movable masses  146  and  148 , respectively. Between the detectors and movable masses is a lens system  144 .  FIG. 16-B  illustrates schematically a configuration of a light source  150  and detectors  140  and  142  in a cross-sectional view.  FIG. 16-C  shows a schematic top view of movable masses  146  and  148  along with the cantilevers and stationary masses  143  and  145 . Light source  150  emits a light beam which impinges onto the movable and stationary masses. A pair of beam portions is reflected by masses  143  and  146 , while the other pair by masses  145  and  148 . 
   Referring now to  FIG. 16-A  and  16 -B, the detectors are arranged such that their light receiving areas (not shown) are close to each other and to a light emitting spot  152 . As a consequence, when a beam from source  150  impinges onto the masses and is reflected back, it reaches the detectors. Furthermore, the detectors are arranged such that a pair of the beam portions reflected by masses  143  and  146  is transmitted to detector  140 , and the other pair reflected by  145  and  148  is transmitted to detector  142 . Thus, signals received by detectors  140  and  142  may be used for differential amplification. 
   FIGS.  17 -A and  17 -B—Embodiment of MOEMS Accelerometer Using Planar Waveguides 
     FIG. 17-A  schematically shows a top view of an embodiment of MOEMS accelerometer which employs planar waveguides to transmit a light beam. A beam from light source  118  is coupled into a single-mode waveguide channel  114 . The beam passes through a Y-junction waveguide beam splitter  110  and a single-mode waveguide channel  108  and comes out from a waveguide end  120 . The beam then impinges onto a movable mass  106  and a stationary mass  104  and is reflected back. Part of the reflected beam is coupled into waveguide channel  108 , transmitted through splitter  110  and a single-mode waveguide channel  112 , and finally to a detector  116 . 
   Like mass  28  in  FIG. 3-A , mass  106  is attached to a cantilever  102  and the cantilever to a fixed end  100 . A cross-sectional view along line AA′ is schematically depicted in  FIG. 17-B , where it can be seen the structure is disposed on a substrate  126 . The reflected beam contains two beam portions bounced back by mass  106  and  104  respectively. The accelerometer has principles the same as the embodiment in  FIG. 3-A . It detects acceleration in a direction parallel to channel  108  in the waveguide plane. 
   Waveguide end  120  is preferred to have anti-reflection features to reduce noise and optical power loss. End  120  may be coated with anti-reflection coating for such purpose, or it may be fabricated to have an angled surface, where the surface normal has an angle with respect to the direction of beam propagation. An angled end surface reflects a beam in a direction such that the reflected beam is a leaky wave in the waveguide. 
   FIGS.  18  to  21 —Embodiments of MOEMS Accelerometer Using Planar Waveguide 
     FIG. 18  shows schematically a top view of an embodiment of MOEMS accelerometer using planar waveguide and differential measurement. Like the one in  FIG. 17-A , all the waveguides used here are of single mode. A light source  165  emits a beam which is coupled into a waveguide channel  168 . The beam is split by a Y-junction beam splitter  173  into two beams. Then the two beams respectively pass through Y-junction splitters  171  and  172 , enter waveguide channels  162  and  164 , and are reflected by two accelerometer sub-structures. The sub-structures contain a shared stationary mass  174 , cantilevers  154  and  160 , and movable masses  156  and  158 . 
   A beam from channel  162  is reflected by masses  156  and  174 . Part of the reflected beam is coupled back into channel  162 . The reflected beam then passes through splitter  171 , enters a waveguide channel  166 , and reaches a detector  161 . Similarly, part of a beam reflected by masses  174  and  158  passes through channels  164  and  170  and reaches a detector  163 . The signals received by detectors  161  and  163  may be used for differential amplification. 
     FIG. 19  illustrates schematically a top view of yet another MOEMS accelerometer embodiment using planar waveguide, which contains a cantilever  190 , a movable mass  186 , and a stationary mass  188 . In contrast to the setup in  FIG. 17-A , masses  186  and  188  are separated by a much larger distance and a 2×2 waveguide beam splitter  196  is employed. Because of splitter  196 , a beam from light source  118  is split into two beams after traveling along a waveguide channel  194 . The two beams are transmitted through waveguide channels  191  and  192  and reflected by masses  186  and  188  respectively. The two reflected beams enter channels  191  and  192  and are combined by splitter  196 . Part of the combined beam is transmitted to a waveguide channel  193  and sensed by detector  116 . Compared to the setup in  FIG. 17-A , the scheme here is more flexible in terms of fabricating the movable and fixed masses, though at a cost of a larger footprint and it needs extra effort to match the two optical paths. 
   As shown in a schematic top view in  FIG. 20 , another MOEMS accelerometer embodiment makes use of the schemes in  FIG. 17-A  and combines two accelerometers so that it can sense acceleration in two dimensions. A Y-junction splitter  202  splits a beam from light source  165  into two beams. One beam passes through a Y-junction splitter  201  and heads for an accelerometer substructure  198 , while the other beam goes through a Y-junction splitter  203  and impinges onto the other accelerometer substructure  200 . The accelerometer sub-structure contains a movable mass, a cantilever, and a stationary mass as that in  FIG. 17-A . Like the embodiments discussed before, substructure  198  reflects a beam back to the waveguide, and the reflected beam is partially transmitted to a detector  161  and provides data for acceleration in the Y direction. Meanwhile, a detector  163  measures acceleration in the X direction. 
   With reference to a schematic top view in  FIG. 21 , yet another embodiment of waveguide MOEMS accelerometer employs transmission, instead of reflection as in above discussions, to detect movement of a movable mass. A beam from light source  118  is coupled into a waveguide channel  306 . The beam is then transmitted by the channel to impinge onto a movable mass  316  and a stationary mass  310 , which are arranged between channel  306  and the other waveguide channel  308 . After passing through masses  316  and  310 , the beam is coupled into channel  308  and heads for detector  116 . When mass  316  is subjected to acceleration, a cantilever  312 , having a fixed end  314 , is bent and mass  316  tilts. As in  FIGS. 11 and 12-A , tilting of mass  316  results in change of the optical path length for a passing beam portion and interference is used to measure the acceleration. 
   FIG.  22 —Embodiment of MOEMS Pressure Sensor 
     FIG. 22  illustrates schematically a cross-sectional view of a MOEMS sensor for pressure measurements of fluid. An optical fiber  220  is connected to a light source and a detector (not shown). Fiber  220  may be replaced by a planar waveguide or an assembly of closed disposed light source and detector like the one shown before, where a light emitting spot is proximate to a light receiving area. A cavity  228  is enclosed by a membrane  232  and two ring-shaped cavity elements  224  and  230 . Inside cavity  228 , there are a stationary mass  222  and a movable mass  226  which is disposed on membrane  232  and moves with it. 
   The embodiment in  FIG. 22  has the same principles as a reflection-type MOEMS pressure sensor or accelerometer. When a beam impinges onto masses  222  and  226 , the reflection creates two beam portions. The beam portions are partially coupled back into fiber  220  and transmitted to the detector. Interference intensity between the beam portions is dependable upon height difference between masses  222  and  226 . Any pressure change outside of membrane  232  causes displacement of the membrane. As a result, pressure can be measured by an optical interference method. Having a smooth membrane surface outside, the scheme may be used to measure pressure caused by fluid flow. To reduce influence on mass  222  by acceleration, mass  222  may be made thicker or to be connected to element  224 . 
   CONCLUSION, RAMIFICATIONS, AND SCOPE 
   Thus it can be seen that I have used a light source, a detector, a stationary mass, and a movable mass to provide a MOEMS accelerometer and a MOEMS pressure sensor. 
   The MOEMS accelerometer and MOEMS pressure sensor have the following advantages: 
   The ability to obtain acceleration or pressure measurements at high-sensitivity and high-resolution by optical interferometric methods. 
   The optical interferometric structure which is relatively simpler and easier to fabricate than the current ones. 
   Although the description above contains many specificities, these should not be construed as limiting the scope of the invention but as merely providing illustrations of some of the presently preferred embodiments. Numerous modifications, alternations, and variations will be obvious to those skilled in the art. 
   For example, a gyro can be made by using several MOEMS accelerometers, since a gyro requires acceleration value along different directions at the same time. 
   For all schemes, an isolator may be added to reduce unwanted feedback to a light source. 
   Phase tuning mechanism may be added to channel  192  of the embodiment in  FIG. 19  to control interference of the two returned beams. For example, the waveguide may be fabricated using electro-optical materials. And fixed mass  188  may be replaced by a flat reflective end of channel  192 . 
   The two-dimensional accelerometer disclosed may be combined with another accelerometer for three-dimensional acceleration measurements. 
   The embodiment of two-dimensional acceleration measurement in  FIG. 20  may be modified for use of differential amplification by employing schemes depicted in  FIG. 18 . 
   In  FIG. 21 , waveguide channels  306  and  308  may be replaced by two single-mode optical fibers. 
   In  FIG. 22 , while the movable and stationary masses remain the same, the cavity may be arranged to be on the other side of membrane  232 . Compared with the embodiment in  FIG. 10 , the merit of using mass  222  is of closeness of the movable and stationary masses for a pressure sensor, which makes the device more compact. 
   Lastly, the accelerometer and pressure sensor schemes as discussed may be used to make vibration sensors and shock sensors. The same principles may also be used to measure gravity, radiation, temperature, electrostatic fields, magnetic fields, chemicals, or combinations. 
   Therefore the scope of the invention should be determined by the appended claims and their legal equivalents, rather than by the examples given.