Abstract:
A multiple source array for illuminating an object including: a reflective mask having an array of spatially separated apertures; at least one optic positioned relative to the mask to form an optical cavity with the mask; and a source providing electromagnetic radiation to the optical cavity to resonantly excite a mode supported by the optical cavity, wherein during operation a portion of the electromagnetic radiation built-up in the cavity leaks through the mask apertures towards the object.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority from provisional application Ser. No. 60/221,091 filed Jul. 27, 2000 by Henry A. Hill entitled “Multiple-Source Arrays with Optical Transmission Enhanced by Resonant Cavities,” the contents of which is incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     Efficient, controlled conveyance of optical energy through apertures in otherwise opaque materials is an important aspect of many optical measurement instruments. This observation is especially applicable to near-field microscopy, which employs apertures smaller than a free space optical wavelength of an optical beam used in the near-field microscopy, hereinafter referred to as sub-wavelength apertures, to achieve imaging with high spatial resolution. The low optical efficiency, typically of the order 10 −4  or lower, of sub-wavelength probes used as near-field scanning probes can have a negative impact on signal-to-noise ratios and measurement bandwidth. 
     SUMMARY OF THE INVENTION 
     The invention features systems and methods for near-field, interferometric microscopy and interferometric, confocal microscopy in which a resonant optical cavity is formed adjacent an aperture or array of apertures to enhance transmission of a probe beam, e.g., a near-field probe beam, through the aperture or array of apertures. The apertures may be used in either reflective or transmissive microscopy systems. Furthermore, the microscopy systems using the aperture or array of apertures may be designed to investigate the profile of a sample, to read optical date from a sample, and/or write optical date to a sample. 
     In general, in one aspect, the invention features a multiple source array for illuminating an object. The multiple source array includes: a reflective mask having an array of spatially separated apertures; at least one optic positioned relative to the mask to form an optical cavity with the mask; and a source providing electromagnetic radiation to the optical cavity to resonantly excite a mode supported by the optical cavity. During operation a portion of the electromagnetic radiation built-up in the cavity leaks through the mask apertures towards the object. Typically, the optical cavity is designed to be stable for resonantly excited mode. 
     Embodiments of the multiple source array may include any of the following features. 
     The excited mode may have transverse dimensions at the reflective mask that are substantially larger than a transverse dimension of each aperture. For example, the transverse dimensions of the excited mode at the reflective mask may be more than 50 times larger, or even more than 500 times larger than the transverse dimension of each aperture. 
     Each aperture may have a transverse dimension smaller than the vacuum wavelength of the electromagnetic radiation provided by the source. 
     Each aperture may have a transverse dimension comparable to the vacuum wavelength of the electromagnetic radiation provided by the source. 
     The apertures may be formed by holes in the reflective mask. 
     The apertures may be formed by dielectric regions in the reflective mask. 
     Each aperture may include a dielectric region defining a waveguide having transverse dimensions sufficient to support a propagating mode of the electromagnetic radiation. During operation the waveguides couple the electromagnetic energy built-up in the cavity between opposite sides of the mask. The reflective mask may further include an end mask portion adjacent the object, wherein each aperture further includes a secondary aperture formed in the end mask portion and aligned with the corresponding waveguide. In such cases, each secondary aperture has a transverse dimension smaller than the transverse dimensions of the corresponding waveguide. For example, the transverse dimension of each secondary aperture may be smaller than the vacuum wavelength of the electromagnetic radiation provided by the source. Furthermore, the reflective mask may include a reflective dielectric stack surrounding the waveguides, and the end mask portion may include a metal layer providing the secondary apertures. Furthermore, in some cases, each waveguide defines a second optical cavity between the opposite sides of the mask, and the length of each waveguide is selected to be resonant with the corresponding propagating mode of the electromagnetic radiation. 
     The reflective mask may include a reflective dielectric stack. Furthermore, the reflective dielectric stack may be adjacent the optical cavity and the reflective mask may further include an antireflection coating adjacent the object. 
     The multiple source array may further include a dielectric material contacting the mask in the cavity. For example, the dielectric material may include an Amici lens. The optical cavity may be a linear optical cavity. For example, the at least one optic may be one optic (e.g., a mirror or a lens), and the linear optical cavity is formed by two surfaces, the first surface being defined by the optic and the second surface being defined by the interface between the reflective mask and dielectric material. Furthermore, the dielectric material may fill the space between the two surfaces and the first surface is defined by the interface between the optic and the dielectric material. 
     In other embodiments, the at least one optic may be two optics and the cavity may be a folded cavity formed by three surfaces, the first surface being defined by the first optic, the second surface being defined by the second optic, and the third surface being defined by the interface between the reflective mask and a dielectric material contacting the mask in the cavity. For example, the first and second surfaces may define the end surfaces for the folded optical cavity. 
     The optical cavity may also be a ring cavity. For example, the at least one optic may include two optics and the ring cavity may be formed by three surfaces, the first surface being defined by the first optic, the second surface being defined by the second optic, and the third surface being defined by the interface between the reflective mask and dielectric material. 
     The multiple source array may further include an active feedback system for maintaining the resonance between the optical cavity and the electromagnetic radiation provided by the source. For example, the active feedback system may include an electronic controller that causes the source to change the wavelength of the electromagnetic radiation in response to a servo signal derived from a portion of the electromagnetic radiation reflected from the optical cavity. Also, the system may include a dielectric material at least partially filling the optical cavity, and the active feedback system may include a temperature controller coupled to the dielectric material and an electronic controller that causes the temperature controller to change the temperature of the dielectric material in response to a servo signal derived from a portion of the electromagnetic radiation reflected from the optical cavity. Furthermore, the active feedback system may include a transducer coupled to one of the optics that form the optical cavity and an electronic controller that causes the transducer to dither the coupled optic in response to a servo signal derived from a portion of the electromagnetic radiation reflected from the optical cavity. 
     In another aspect, the invention features a microscopy system for imaging an object. The microscopy system includes: the multiple source array described above; a multi-element photo-detector; and an imaging system positioned to direct a return beam to the multi-element detector, wherein the return beam includes electromagnetic radiation leaked to the object and scattered/reflected back through the apertures. The microscopy system may further include a pinhole array positioned adjacent the photo-detector, wherein each pinhole is aligned with a separate set of one or more detector elements, and wherein the imaging system produces a conjugate image of each aperture on a corresponding pinhole of the pinhole array. In addition, the microscopy system may further include an interferometer which separates the electromagnetic radiation from the source into a measurement beam which is directed to the optical cavity and a reference beam which is directed along a reference beam path and combined with the return beam to interfere at the multi-element photo-detector. 
     In another aspect, the invention features a microscopy system for imaging an object, the microscopy system including: the multiple source array described above; a multiple detector array including an array of spatially separated apertures; a multi-element photo-detector; and an imaging system positioned to direct a signal beam to the multi-element detector, wherein the signal beam includes electromagnetic radiation leaked to the object and transmitted by the object through the apertures of the detector array. The apertures of the source array may be aligned with the apertures of the detector array. The microscopy system may further include a pinhole array positioned adjacent the photo-detector, wherein each pinhole is aligned with a separate set of one or more detector elements, and wherein the imaging system produces a conjugate image of each aperture of the detector array on a corresponding pinhole of the pinhole array. In addition, the microscopy system may further include: an interferometer which separates the electromagnetic radiation from the source into a measurement beam which is directed to the optical cavity and a reference beam which is directed along a reference beam path and combined with the signal beam to interfere at the multi-element photo-detector. 
     In general, in another aspect, the invention features a source for illuminating an object. The source includes: a reflective mask having at least one aperture; and at least one optic positioned relative to the mask to form a stable optical cavity with the mask, wherein during operation a portion of electromagnetic energy built-up in the cavity couples through the mask aperture towards the object. The source may further include any of the features described above for the multiple source arrays. 
     In general, in another aspect, the invention features a method for illuminating an object with multiple sources, the method including: resonantly exciting a mode of a stable optical cavity; and coupling electromagnetic radiation out of the optical cavity towards the object through an array of apertures in one of the optics that define the cavity, wherein transverse dimensions of the excited mode are substantially larger than a transverse dimension of each aperture. The method may further include features corresponding to any of the features described above for the multiple source array. 
     Confocal and near-field confocal, microscopy systems are also described in the following, commonly-owned applications: Ser. No. 09/631,230 filed Aug. 2, 2000 by Henry A. Hill entitled “Scanning Interferometric Near-Field Confocal Microscopy,” and the corresponding PCT Publication WO 01/09662 A2 published Feb. 8, 2001; Provisional Application Ser. No. 60/221,019 filed Jul. 27, 2000 by Henry A. Hill and Kyle B. Ferrio entitled “Multiple-Source Arrays For Confocal And Near-Field Microscopy” and the corresponding Utility application Ser. No. 09/917,402 having the same title filed on Jul. 27, 2001; Provisional Application Ser. No. 60,221,086 filed Jul. 27, 2000 by Henry A. Hill entitled “Scanning Interferometric Near-Field Confocal Microscopy with Background Amplitude Reduction and Compensation” and the corresponding Utility application Ser. No. 09/917,399 having the same title filed on Jul. 27, 2001; Provisional Application Ser. No. 60/221,287 by Henry A. Hill filed Jul. 27, 2000 entitled “Control of Position and Orientation of Sub-Wavelength Aperture Array in Near-field Scanning Microscopy” and the corresponding Utility application Ser. No. 09/917,401 having the same title filed on Jul. 27, 2001; and Provisional Application Ser. No. 60/221,295 by Henry A. Hill filed Jul. 27, 2000 entitled “Differential Interferometric Confocal Near-Field Microscopy” and the corresponding Utility application Ser. No. 09/917,276 having the same title filed on Jul. 27, 2001; the contents of each of the preceding applications being incorporated herein by reference. Aspects and features disclosed in the preceding provisional applications may be incorporated into the embodiments described in the present application. 
     Embodiments of the invention may include any of the following advantages. 
     One advantage is enhanced transmission of an optical beam through an array of wavelength and/or sub-wavelength apertures. 
     Another advantage is the control of the phase of an enhanced transmission of an optical beam through an array of wavelength and/or sub-wavelength apertures. 
     Another advantage is the control of an enhanced transmission of an optical beam through an array of wavelength and/or sub-wavelength apertures by adjustment of the resonant frequency of an optical cavity for the optical beam using one or more of electro-mechanical transducers, electro-optical phase modulators, and thermal expansion effects. 
     Another advantage is excitation of an optical mode of transmission through apertures of an array of wavelength and/or sub-wavelength apertures comprising optical waveguides. 
     Another advantage is the generation of relative phase shifts at high frequencies between a reference beam and an optical beam transmitted through an array of wavelength and/or sub-wavelength apertures with an enhanced transmission. 
     Another advantage is that a wavelength of a source of a near-field probe beam may be in the ultraviolet, visible, or the infrared. Furthermore, the source may comprise two or more different wavelengths. 
     Another advantage is an interferometric profiler based on interferometry of near-field beams. 
     Another advantage is that the interferometric analysis of the near-field signal beam can improve the signal-to-noise of the near-field information, e.g., the complex amplitudes of near-field beams scattered/reflected by a sample. 
     Another advantage is that the interferometric analysis can reveal changes in the phase or complex amplitude of near-field signal beams as a function of sample location. 
     Another advantage is that the confocal features of the systems and methods can remove background contributions from the signal of interest. 
     Another advantage is that the systems and methods can operate in a continuous scan mode with a pulsed input optical beam. 
     Another advantage is that in embodiments operating in a reflection mode, each mask aperture couples a near-field probe beam to the sample and couples a near-field signal beam toward the detector. Thus, each mask aperture is both a transmitter and receiver for a corresponding near-field beam, thereby improving lateral resolution. As a further result, the directions of propagation of the components of each near-field probe beam that produce a corresponding near-field signal beam at a given volume section of the sample are substantially the same, thereby simplifying an inverse calculation for properties of the sample using the complex amplitude of the near-field signal beam from the interference signal(s). 
     Another advantage is that the sample can be profiled using substantially low order electric and magnetic multipole near-field sources, e.g., near-field probe beam sources including an electric dipole and two different orthogonal orientations of a magnetic dipole. 
     Another advantage is that effects of interference terms caused by a background beam scattered and/or reflected from the mask apertures can be compensated. The interference terms can include interference between the background beam and the reference beam, and the background beam and the near-field signal beam. 
     Another advantage is that statistical errors in measured amplitudes and phases of the near-field signal beams can be substantially the same as statistical errors based on Poisson statistics of the reflected/scattered near-field probe beams. In other words, the measured amplitudes and phases are not significantly degraded by the presence of background signals. 
     Another advantage is that the sample properties can be analyzed by using multiple wavelengths. 
     Another advantage is that the separation between the mask and the sample can be varied to measure the radial dependence of the amplitudes and phases of the near-field signal beams. 
     Another advantage is that the relative lateral position of the mask and the sample can be varied to measure the angular dependence of the amplitudes and phases of the near-field signal beams. 
     Another advantage is that the spatial resolution of the system is defined primarily by the dimensions of the mask apertures and their distance from the sample, and is only weakly dependent on the optical system imaging the near-field signal beams emerging from the mask apertures onto the detector array. 
     Another advantage is that the sample scanning may be implemented in a “step and repeat” mode or in a continuous scan mode. 
     Another advantage is that a source of the near-field probe beam may be a pulsed source, which may be synchronized with the sample scanning. 
     Another advantage is that by using a mask with an array of apertures, multiple interference terms can be measured substantially simultaneously for a one-dimensional or a two-dimensional array of locations on the sample. Furthermore, background noise in the multiple interference terms are correlated to one another. 
     Another advantage is that a given state of magnetization at the region of the sample illuminated by the near-field probe beam can be measured based on the polarization rotation of the near-field signal beam. 
     Another advantage is that the system can be used to write to an optical data storage medium such as a magneto-optical material. 
     Another advantage is that the system can profile a surface and internal layers near the surface of an object being profiled/imaged without contacting the object. 
     Another advantage is that either optical heterodyne or homodyne techniques may be used to measure amplitudes and phases of interference terms between the reference beam and the near-field signal beams. 
     Another advantage is that the complex refractive index of the sample at a location illuminated by the near-field probe beam can be determined from measured arrays of interference data corresponding to the near-field signal beams, wherein the dimensionality of the arrays may comprise one or two dimensions corresponding to one and two dimensions of space, a dimension for the spatial separation of the mask and the sample, a dimension for each of wavelength of components of the near-field probe beam source, and a dimension for the multipole characterization of the near-field probe beam. 
     Another advantage is that multiple layers of optical data stored on and/or in an optical storage medium can be read by measuring interference data for multiple separations between the mask and the sample. 
     Another advantage is that multiple layers of optical data stored on and/or in an optical storage medium can be read substantially simultaneously by measuring interference data for multiple wavelengths of the near-field probe beam, and/or different polarizations of the near-field probe beam. 
     Another advantage is that the mask can include sub-wavelength apertures in a sub-wavelength thick conducting layer, wavelength and sub-wavelength Fresnel zone plate(s), microlenses, and/or gratings to alter the properties of the near-field probe beam(s). 
     Another advantage is that a change in temperature of a site in or on the sample can be detected as a corresponding change in the complex value of the index of refraction. 
     Other features, aspects, and advantages follow. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the drawings, wherein like reference characters denote similar elements throughout the several views: 
         FIG. 1  illustrates, in schematic form, a first embodiment of the present invention; 
         FIG. 2   a  illustrates, in schematic form, an optical cavity used in the first embodiment; 
         FIG. 2   b  illustrates, in schematic form, a wavelength or sub-wavelength aperture array used in the first embodiment; 
         FIG. 2   c  illustrates, in schematic form, a reference object used in the first embodiment; 
         FIG. 2   d  illustrates, in schematic form, a reference object wavelength or sub-wavelength aperture array used in the first embodiment 
         FIG. 2   e  illustrates, in schematic form, a detector aperture array used in the first embodiment; 
         FIG. 2   f  illustrates, in schematic form, an optical cavity used in a first variant of the first embodiment; 
         FIG. 2   g  illustrates, in schematic form, a reference object used in a first variant of the first embodiment; 
         FIG. 3  illustrates, in schematic form, a second embodiment of the present invention; 
         FIG. 4  illustrates, in schematic form, a third embodiment of the present invention; 
         FIG. 5  illustrates, in schematic form, a fourth embodiment of the present invention; 
         FIG. 6   a  illustrates, in schematic form, an optical cavity used in the fourth embodiment; 
         FIG. 6   b  illustrates, in schematic form, a wavelength or sub-wavelength aperture array used in the fourth embodiment; 
         FIG. 7  illustrates, in schematic form, a fifth embodiment of the present invention; 
         FIG. 8   a  illustrates, in schematic form, an optical cavity used in the fifth embodiment; and 
         FIG. 8   b  illustrates, in schematic form, the relationship between a standing wave pattern and a wavelength or sub-wavelength aperture array used in the fifth embodiment. 
         FIG. 9  illustrates, in schematic form, a mask array having formed by waveguide elements in an reflective dielectric stack. 
         FIG. 10  illustrates, in schematic form, an embodiment of the invention operating in a transmission mode. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Embodiments of the present invention comprise enhanced transmission of an optical beam through an aperture or arrays of apertures. For near-field applications one or more of the apertures may have a dimension or dimensions less than wavelength of the free-space incident beam, e.g., a sub-wavelength aperture. In other applications, one or more of the apertures may have a dimension or dimensions less than, comparable to, or greater than the wavelength of the free-space incident beam, e.g., wavelength apertures. 
     The enhanced transmission is achieved by use of optical cavities. The embodiments further comprise scanning interferometric near-field confocal microscopes operating in either a reflection or transmission mode. 
     While the apparatus of the present invention has application for a wide range of radiation sources, the following description is taken, by way of example, with respect to an optical measuring system in which the incident beam is a beam of electromagnetic radiation, e.g., an optical beam. In further embodiments, for example, the beam incident on the aperture or arrays of apertures can include an acoustic radiation beam, an electron beam, and an atomic beam. 
     The source of optical beams used by embodiments of the present invention include CW and pulsed sources in different combinations with single and multiple wavelength sources. The optical cavities are used in generation of enhanced transmission through arrays of wavelength and/or sub-wavelength apertures for both near-field probe beams and reference beams. 
     Also, while the apparatus of the present invention has application for a wide range of imaging systems, the following description is taken, by way of example, with respect to interferometric confocal near-field microscopy measuring systems. Optical cavities as used herein includes, but is not limited to, use in scanning and step-and-repeat interferometric near-field confocal microscopy systems and scanning and step-and-repeat confocal and interferometric confocal microscopy systems. 
     Referring to the drawings in detail,  FIG. 1  depicts in schematic form the first embodiment of the present invention. As shown in  FIG. 1 , the first embodiment comprises an interferometer, a source  10 , object material  112 , object material chuck  160 , chuck stage  162 , translator  164 , detector  116 , an optical cavity generally indicated at element number  130 , and reference object  130 R. The configuration of the interferometer is known in the art as a Michelson interferometer, and is shown as a simple illustration. Other forms of interferometer known in the art such as a polarized Michelson interferometer and as described in an article entitled “Differential Interferometer Arrangements for Distance and Angle Measurements: Principles, Advantages, and Applications,” by C. Zanoni (VDI Berichte NR. 749, pp. 93-106, 1989) may be incorporated into the apparatus of  FIG. 1  without departing from the spirit and scope of the present invention. Other forms of scanning interferometric near-field confocal microscopes, such as those described in the previously mentioned, commonly owed provisional applications incorporated herein by reference, may be incorporated into apparatus of  FIG. 1  without departing from the spirit and scope of the present invention. 
     Light source  10  such as a laser can be any of a variety of lasers. For example, the laser can be a gas laser, e.g., a HeNe laser, stabilized in any of a variety of conventional techniques known to those skilled in the art, see for example, T. Baer et al., “Frequency Stabilization of a 0.633 μm He—Ne-longitudinal Zeeman Laser,”  Applied Optics,  19, 3173-3177 (1980); Burgwald et al., U.S. Pat. No. 3,889,207, issued Jun. 10, 1975; and Sandstrom et al., U.S. Pat. No. 3,662,279, issued May 9, 1972. Alternatively, the laser can be a diode laser frequency stabilized in one of a variety of conventional techniques known to those skilled in the art, see for example, T. Okoshi and K. Kikuchi, “Frequency Stabilization of Semiconductor Lasers for Heterodyne-type Optical Communication Systems,”  Electronic Letters,  16, 179-181 (1980) and S. Yamaqguchi and M. Suzuki, “Simultaneous Stabilization of the Frequency and Power of an AlGaAs Semiconductor Laser by Use of the Optogalvanic Effect of Krypton,”  IEEE J. Quantum Electronics, QE- 19, 1514-1519 (1983). 
     For certain of the embodiments disclosed herein, light sources corresponding light source  10  may also be a pulsed source. There are several different procedures for producing a pulsed source [see Chapter 11 entitled “Lasers”,  Handbook of Optics,  1, 1995 (McGraw-Hill, New York) by W. Silfvast]. There may be a restriction on the pulse width. For example, the pulse width may be based on a consideration of the spatial resolution required for a scanning end-use application and/or enhancement properties of the first embodiment as subsequently described. 
     For the first embodiment, light source  10  is preferably a monochromatic point source or a spatially incoherent source of radiation across surface of the source, preferably a laser or like source of coherent or partially coherent radiation, and preferably polarized. Light source  10  emits input beam  12 . As shown in  FIG. 1 , input beam  12  enters collimating lens  14  to form input beam  16 . Input beam  16  is transmitted by a phase retardation plate  18  as input beam  20 . The plane of polarization of input beam  20  is rotated by phase retardation plate  18  to be either parallel or orthogonal to the plane of FIG.  1 . However, other orientations of the plane of polarization of input beam  20  may be beneficially used in certain end-use applications. The function of phase retardation plate  18  is controlled by signal  128  from electronic controller, signal processor, and computer  200 . 
     The specific device used for the source of beam  12  will determine the diameter and divergence of beam  12 . For some sources, e.g., a diode laser, it may be necessary to use conventional beam shaping optics, e.g., a conventional microscope objective and/or anamorphic prisms, to provide beam  12  with a suitable diameter and divergence for elements that follow. When the source is a HeNe laser, for example, beam shaping optics may not be required. 
     Beam  16  is shown in  FIG. 1  as a collimated beam but may be a diverging or a converging beam depending on requirements of an end-use application. 
     Input beam  20  is incident on a non-polarizing beam splitter  102  and a first portion thereof is reflected as a measurement beam  22 . A second portion of input beam  20  incident on beam splitter  102  is transmitted as a reference beam  50 . A portion of measurement beam  22  is reflected by non-polarizing beam splitter  104  to form measurement beam  24  after reflection by mirror  112 A. Beam  24  is incident on optical cavity  130 . The reflection coefficient for non-polarizing beam splitter  104  is preferably ≳95% so as not to significantly reduce the intensity of beam  24 . 
     The propagation of measurement beam  24  through the optical cavity  130  is shown schematically in an expanded form in  FIG. 2   a . In the presently described embodiment, element  132  is an Amici type objective lens. Measurement beam  24  is focused by lenses  122  and  132  to a beam spot at aperture-array element  142  that encompasses an array of at least one wavelength or sub-wavelength aperture and at least one wavelength or sub-wavelength scattering site in aperture-array element  142 . Aperture-array element  142  shown schematically in  FIG. 2   b  in an expanded form is a conducting layer (e.g., a reflective layer) on a surface  143  of Amici type lens  132 . 
     The wavelength or sub-wavelength apertures and the wavelength or sub-wavelength scattering sites are elements  30  and  32 , respectively, as indicated in  FIG. 2   b . Wavelength and/or sub-wavelength scattering sites  32  are preferably non-transmitting conducting elements with a complex index of refraction different from the complex index of refraction of the conducting material of aperture-array element  142 . The complex indices of refraction are different so that elements  32  effectively serve as wavelength or sub-wavelength scattering sites. The diameter of elements  30  and  32  is a with a&lt;λ 1 , preferably a&lt;&lt;λ 1 , where λ 1  is the wavelength of measurement beam  24 . The separation of elements  30  and  32  is b with b&gt;a, preferably b&gt;&gt;a. The thickness of conducting material of aperture-array element  142  is of the order of 20 nm and chosen so that the fraction of a beam transmitted by sections of aperture-array element  142  not containing wavelength or sub-wavelengths  30  is &lt;&lt;1. 
     The relative spacing of elements  30  in aperture-array element  142  may be further selected to minimize the effect of one wavelength or sub-wavelength aperture on the transmission properties of a second wavelength or sub-wavelength aperture. 
     The diameters of wavelength or sub-wavelength apertures  30  need not be restricted to a single diameter as shown schematically in  FIG. 2   b  but may beneficially comprise two or more diameters for an end-use application. Further, the shape of wavelength or sub-wavelength apertures  30  may comprise shapes other than circular, e.g., a square or rectangle, without departing from the spirit and scope of the present invention. 
     The spacing of wavelength or sub-wavelength apertures  30  need not be restricted to a single value as shown schematically in  FIG. 2   b  but may beneficially comprise two or more different spacings for an end-use application without departing from the spirit and scope of the present invention. 
     Further, the arrangement of wavelength or sub-wavelength apertures  30  may be arranged in various geometric patterns or random patterns without departing from the spirit and scope of the present invention. 
     The apertures  30  in element  142  can be formed as holes in a mask or as transmissive dielectric regions in an otherwise non-transmissive mask, e.g., transmissive vias in an otherwise reflective element. Moreover, the dielectric material in element  142  defining the apertures  30  can form a waveguide or optical cavity that enhances the transmission of the near-field probe beam to the sample. See, e.g., the previously cited application “Multiple-Source Arrays For Confocal And Near-Field Microscopy.” Furthermore, in the presently described embodiment, the mask portion of element  142  is described as conducting to indicate that it is reflective. In other embodiments, element  142  is not necessarily conductive, but is, generally, not transmissive, with the coupling of the near-field probe beams to the sample being accomplished by the apertures  30  in element  142 . 
     For example, in some embodiments, the structure of element  142  at each aperture  30  may take the form of element  910  shown in FIG.  9 . 
     In particular, element  910  includes a reflective dielectric stack  920  and an end mask portion  930  having an array of secondary apertures  932 . Each aperture  30  includes a waveguide  922  formed by a dielectric material  924  extending through dielectric stack  920  and the secondary aperture  932 . Furthermore, in some embodiments the end mask portion may provide more than one secondary aperture for with each waveguide. As is known in the art, dielectric stack  920  may be formed by alternating layers of dielectric material having refractive indices n 1  and n 2 . Furthermore, dielectric material  924  forming waveguide  922  may have an refractive index n 3 , such that n 3 &gt;n 1  and n 3 &gt;n 2 . End mask portion  930  may be formed by a metal layer, and secondary aperture  932  may be selected to be a sub-wavelength aperture. In other words, secondary aperture may have a transverse dimension smaller than that necessary to support a propagating mode in dielectric material  924 . 
     The resulting structure has the advantage of providing a highly reflective interface (that formed by the reflective dielectric stack) at surface  143  of the optical cavity, thereby enhancing the radiation build-up in cavity  130 . Waveguide  922  couples radiation from optical cavity  130  to the opposite side of dielectric stack  920  where it is incident on end mask portion  930  and radiates to the object through sub-wavelength secondary aperture  932 . 
     Furthermore, to suppress multiple reflections between the object and the surface of element  910  nearest the object, element  910  may further include an anti-reflection layer  940  formed on the surface of element  910  nearest the object. For example, the anti-reflection layer  940  may surround end mask portion  930  and waveguide  922  as shown in FIG.  9 . The anti-reflection layer  940  may be formed by some combination of dielectric and/or metal layers. Moreover, element  910  may further include a metal layer  950  sandwiched between dielectric stack  920  and anti-reflection layer  940  to minimize their interaction between. 
     One example of a suitable series of layers for the anti-reflection coating is as follows: a first 51 nm layer of silicon dioxide, a second layer 6 nm layer of Beryllium, a third 51 nm layer of silicon dioxide, followed by a fourth 50 nm layer of Aluminum on a silicon dioxide substrate, wherein the coating is designed to prevent reflections from an interface between the first layer and air. 
     Also, waveguide  922  may be designed to form a second cavity that re-circulates at least some of the radiation that would otherwise be scattered by secondary aperture  932 . In such cases, the length of waveguide  922  is selected to cause the second cavity to be resonant, or at least substantially resonant, at the wavelength of the radiation. 
     Additional embodiments of the invention may include element  142  having one or more those features described in connection with element  910 . The wavelength or sub-wavelength apertures may further comprise a Fresnel zone plate or a microlens to alter beneficially in certain end-use applications the transmission through an array of wavelength or sub-wavelength apertures without departing from the spirit and scope of the present invention. In certain other end-use applications, gratings may be added to an array of wavelength or sub-wavelength apertures operating as spatial filters of reflected/scattered or transmitted near-field probe beam(s) to alter properties of the reflected/scattered or transmitted near-field probe beam(s) without departing from the spirit and scope of the present invention. 
     Beam  24  is incident on surface  123  of lens  122 , transmitted by surface  123  and then incident on optical cavity  130 . Optical cavity  130  comprises a highly reflective interface between lens  122  and Amici type lens  132 , Amici type lens  132 , and a reflecting interface between aperture-array element  142  and Amici type lens  132 . Lens  122 , Amici type lens  132 , and aperture-array element  142  are preferably bonded together with an optical grade index matching cement. Surface  133  of Amici type lens  132  has the same surface figure as surface  124  of lens  122  and surface  134  of Amici type lens  132  has the same surface figure as surface  143  of aperture-array element  142  which hereinafter are referred to as interfaces  124  and  143 , respectively (element numbers  133  and  134  are not shown in  FIG. 2   a ). Lens  122  comprises surfaces  123  and  124  with surface  123  preferably antireflection coated for the wavelength of beam  24 . 
     The index of refraction of Amici type lens  132  is preferably selected to be a large value so as to yield a substantially reduced wavelength therein and improved limiting optical resolution. 
     Optical cavity  130  is excited by the measurement beam incident on interface  124  with a corresponding buildup of beam  107  inside optical cavity  130 . The intensity of beam  107  is significantly larger than the intensity of beam  24  and as such can lead to an enhanced transmission through apertures  30 . Control of properties of optical cavity  130  with respect to build up of beam  107  is subsequently described in the description of the first embodiment. 
     A first portion of beam  107  incident on wavelength or sub-wavelength apertures  30  is transmitted as a near-field probe beam. A portion of the near-field probe beam is incident on object material  112  and a portion thereof is reflected and/or scattered back to the wavelength or sub-wavelength apertures  30  and a portion thereof is transmitted as a near-field return probe beam. 
     The spatial separation of adjacent surfaces of object material  112  and aperture-array element  142  is h as indicated in  FIG. 2   b . The value of h is preferably of the order of 2 a  with a lateral resolution approximately equal to h. A second portion of beam  107  incident on wavelength or sub-wavelength apertures  30  is reflected and/or scattered as a first background return beam. A portion of beam  107  incident on wavelength or sub-wavelength scattering sites  32  is reflected and/or scattered as a second background return beam. The near-field return probe beam, the first background return beam, and the second background return beam exit Amici type lens  132  as return beam  34  shown as rays  34 A and  34 B in  FIG. 1  wherein return beam  34  comprises rays between rays  34 A and  34 B. Return beam  34  is collimated by lens  60  as return beam  36 . Return beam  36  is shown as rays  36 A and  36 B in FIG.  1  and beam  36  comprises rays between rays  36 A and  36 B. 
     A portion of reference beam  50  reflected by mirror  112 B and incident on non-polarizing beam splitter  106  is reflected as reference beam  52 . Reference beam  52  is incident on reference object  130 R and a portion thereof is transmitted as transmitted reference beam  54 . Beam  54  is shown as rays  54 A and  54 B in FIG.  1  and beam  54  comprises rays between rays  54 A and  54 B. Beam  54  is collimated by lens  66  and transmitted by phase shifter  64  as a transmitted reference beam  86 . Beam  56  is shown as rays  86 A and  86 B in FIG.  1  and beam  56  comprises rays in between rays  56 A and  56 B. Phase shifter  64  introduces a relative phase shift of χ in the transmitted reference beam  56 . The magnitude of phase shift χ is controlled by control signal  158  from electronic controller, signal processor, and computer  200 . 
     The propagation of reference beam  52  through reference object  130 R is shown schematically in an expanded form in  FIG. 2   c . Reference object  130 R comprises lens  122 R, a dielectric material  132 R, aperture array element  142 R, and an Amici type lens  134 . Reference beam  52  is focused by reference object  130 R to a beam spot at aperture array element  142 R that encompasses an array of wavelength or sub-wavelength apertures in aperture array element  142 R. Aperture array element  142 R is shown schematically in  FIG. 2   d  in an expanded form as an array of wavelength or sub-wavelength apertures  30 R and  32 R on a surface of Amici type lens  134 R. Wavelength or sub-wavelength apertures  30 R and  32 R generate transmitted reference beam components of beam  54  that correspond to wavelength or sub-wavelength elements  30  and  32 , respectively, of element  142 . The spacing b″ of the wavelength or sub-wavelength apertures  30 R and  32 R and the imaging properties of Amici type lens  134 R and of lens  66  are chosen such that wavelength or sub-wavelength apertures  30 R and  32 R and wavelength or sub-wavelength elements  30  and  32 , respectively, are conjugates as seen by a subsequent imaging on to a detector. The diameter a″ of the wavelength or sub-wavelength apertures  30 R and  32 R is chosen to be efficient in generating transmitted reference beam  56  with a diameter substantially the same as the diameter of return beam  36 . The relative transmission of wavelength or sub-wavelength apertures  30 R and  32 R may be the same or beneficially different depending on an end-use application. 
     Reference object  130 R comprises an optical cavity hereinafter referenced as the reference optical cavity. The reference optical cavity is defined by interfaces  124 R and  143 R as illustrated schematically in  FIG. 2   c  and leads to an enhanced transmission of reference beam  52  through wavelength or sub-wavelength aperture array  142 R. The remaining description of wavelength or sub-wavelength apertures  30 R and  32 R is the dame as corresponding portion of the description given for wavelength or sub-wavelength apertures  30 . The description of the properties of the reference optical cavity is substantially the same as the corresponding portions of the description given for the properties of optical cavity  130 . 
     Return beam  36  is incident on beam splitter  100  and a portion thereof is reflected as a return beam component of beam  38 . Beam  38  is shown as rays  38 A and  38 B in FIG.  1  and beam  38  comprises rays between rays  38 A and  38 B. Reflected reference beam  56  is incident on beam splitter  100  and a portion thereof is transmitted as a transmitted reference beam component of beam  38 . Beam  38  is incident on lens  62  and focused as mixed beam  40 . Beam  40  is shown as rays  40 A and  40 B in FIG.  1 . Beam  40  is focused onto a pinhole plane  114  such that a pinhole in image plane  114  is a conjugate image of either one of the wavelength or sub-wavelength apertures  30  or wavelength or sub-wavelength scattering sites  32 . 
     Pinhole plane  114  is shown schematically in  FIG. 2   e . The diameter of the pinholes is c and the spacing between the pinholes is d. The spacing d is equal to the separation b of wavelength or sub-wavelength apertures  30  and wavelength or sub-wavelength scattering sites  32  times the magnification of the imaging system imaging wavelength or sub-wavelength apertures  30  and wavelength or sub-wavelength scattering sites  32  onto corresponding pinholes in pinhole plane  114 . Diameter c is selected to be approximately twice the size of a diffraction limited image of a point object by the imaging system and the spacing d is selected to be larger than c, preferably ≧ to approximately four times the size of a diffraction limited image of a point object by the imaging system. Typical amplitude functions of diffraction limited images of wavelength or sub-wavelength apertures  30  and wavelength or sub-wavelength sites  32  are shown in  FIG. 2   e  as a dashed and solid profiles, respectively. 
     A portion of beam  40  is transmitted by the pinholes in pinhole plane  114  and detected by a detector  116 , preferably by a quantum photon detector [see Section 15.3 in Chapter 15 entitled “Quantum Detectors”,  Handbook of Optics,  1, 1995 (McGraw-Hill, New York) by P. R. Norton]. Detector  116  comprises an array of pixels. The array of pixels may comprise either a pair of pixels, a one dimensional array of pixels, or a two dimensional array of pixels, according to the requirements of an end-use application, with a one-to-one mapping of pinholes in pinhole plane  114  and the pixels of detector  116 . 
     Detector  116  generates an electrical interference signal comprising an array of signal values [S n ] corresponding to the array of pixels. Subscript n is an index indicating an element in the array of signal values [S n ]. The array of signal values [S n ] may comprise a pair of elements, a one-dimensional array comprising at least three elements, or a two-dimensional array depending on an end-use application. Also, in other embodiments, the measurement and reference beam components in beam  38  may have different, e.g., orthogonal, polarizations, in which case a polarizer may be added to mix the polarizations of the measurement and reference beam components in beam  38  to cause the interference signal at detector  116 . 
     The array of signal values [S n ] may be written to a good approximation as
 
[ S   n ]=[( S   D   +S   I ) n ]  (1)
 
where term (S D ) n  represents terms either associated with wavelength or sub-wavelength apertures  30  or associated with wavelength or sub-wavelength sites  32  and term (S I ) n  represents interference cross terms either associated with wavelength or sub-wavelength apertures  30  or associated with wavelength or sub-wavelength sites  32 .
 
     A (S D ) n  term associated with wavelength or sub-wavelength apertures  30  is proportional to the sum of the amplitude magnitudes squared of the corresponding portions of the near-field return probe beam, of the first background return beam, and of the reflected reference beam and interference cross terms between complex amplitudes of the near-field return probe beam and of the first background return beam. A (S D ) n  term associated with wavelength or sub-wavelength sites  32  is proportional to the sum of the amplitude magnitudes squared of the corresponding portions of the second background return beam and of the reflected reference beam. A (S I ) n  term associated with wavelength or sub-wavelength apertures  30  is proportional to the sum of the interference cross terms between complex amplitudes of the near-field return probe beam and of the reflected reference beam and between complex amplitudes of the first background return beam and of the reflected reference beam. A (S I ) n  term associated with wavelength or sub-wavelength sites  32  is proportional to the interference cross term between complex amplitudes of the second background return beam and of the reflected reference beam. 
     Term (S D ) n  is independent of phase shift χ. Term (S I ) n  is a sinusoidal function of phase shift χ and may be written as
 
( S   I ) n =(| S   I |cos(φ+χ)) n   (2)
 
where (|S I |) n  and φ are an amplitude and phase, respectively, related to the complex amplitudes contributing to (S I ) n .
 
     Operation of apparatus of the first embodiment of the present invention depicted in  FIGS. 1 ,  2   a ,  2   b ,  2   c ,  2   d , and  2   e  is based on the acquisition of a sequence of four measurements of arrays of signal values. The sequence of the four arrays of signal values [S n ] 1 , [S n ] 2 , [S n ] 3 , and [S n ] 4  are obtained by detector  116  with phase shifter  64  introducing a sequence of phase shifts χ 0 , χ 0 +π, χ 0 +π/2, and χ 0 +3π/2 radians, respectively, where χ 0  is some fixed value of phase shift χ. The four arrays of signal values [S n ] 1 , [S n ] 2 , [S n ] 3 , and [S n ] 4  are sent to electronic controller, signal processor, and computer  200  as signal  131 , in either digital or analog format, for subsequent processing. 
     Conventional conversion circuitry, i.e., analog-to-digital converters, is included in either detector  116  or electronic controller, signal processor, and computer  200  for converting the four arrays [S n ] 1 , [S n ] 2 , [S n ] 3  and [S n ] 4  to a digital format. Phase shift χ introduced by phase shifter  64  is controlled by signal  158  where signal  158  is generated and subsequently transmitted by electronic controller, signal processor, and computer  200 . Phase shifter  64  can be of an electro-optical type. 
     Next, two arrays of signal value differences [S n ] 1 −[S n ] 2 =[(S I ) n ] 1 −[(S I ) n ] 2  and [S n ] 3 −[S n ] 4 =[(S I ) n ] 3 −[(S I ) n ] 4  are computed by electronic controller, signal processor, and computer  200 . Elements of the arrays of signal value differences corresponding to pixels that are associated with wavelength or sub-wavelength apertures  30  contain substantially with relatively high efficiency only two interference cross terms, a first interference cross term between the complex amplitude of the near-field return probe beam and of the complex amplitude of the reflected reference beam and a second interference cross term between the complex amplitude of the first background return beam and of the complex amplitude of the reflected reference beam. Elements of the arrays of signal value differences corresponding to pixels that are associated with wavelength or sub-wavelength sites  32  contain substantially with relatively high efficiency only the interference cross term between the complex amplitude of the second background return beam and of the complex amplitude of the reflected reference beam. 
     The relatively high efficiency for isolation of effects of amplitudes of beams associated with wavelength or sub-wavelength apertures  30  and wavelength or sub-wavelength sites  32  in the measured signal values is controlled by the choice of parameters c and d. 
     The complex amplitude of the near-field return probe beam is computed by electronic controller, signal processor, and computer  200  from the amplitude of the first interference term between the complex amplitude of the near-field return probe beam and the amplitude of the reflected reference beam. The computation comprises using measured values of the interference cross term between the complex amplitude of the second background return beam and of the complex amplitude of the reflected reference beam to compensate the measured values of elements of signal value differences associated with sub-wavelength apertures  30  for the contribution of the second interference cross term between the complex amplitude of the first background return beam and of the complex amplitude of the reflected reference beam. The computation further comprises using measured values for the amplitude magnitude squared of the portions of the reflected reference beam transmitted by the pinholes of pinhole plane  114  and detected by detector  116 . 
     Next, the plane of polarization of input beam  20  is rotated by 90° by phase retardation element  18  in response to signal  128  from electronic controller, signal processor, and computer  200 . A second set of four arrays of signal values [S n ] 5 , [S n ] 6 , [S n ] 7 , and [S n ] 8  corresponding to measured arrays of signal values [S n ] 1 , [S n ] 2 , [S n ] 3 , and [S n ] 4  are obtained by detector  116 . Arrays of signal value differences [S n ] 1 −[S n ] 2 =[(S I ) n ] 1 −[(S I ) n ] 2  and [S n ] 3 −[S n ] 4 =[(S I ) n ] 3 −[(S I ) n ] 4  are computed by electronic controller, signal processor, and computer  200 . The complex amplitude of the near-field return probe beam for the orthogonally polarized input beam  20  is computed by electronic controller, signal processor, and computer  200  by the same algorithm as used to compute the complex amplitude of the near-field return probe beam for the non-rotated polarization state of input beam  20 . 
     Object material  112  is mounted on an object chuck  160 . The angular orientation and height of object chuck  160  is controlled by three transducers, two of which are shown as  161 A and  161 B, that are attached to chuck stage  162 . The angular orientation and height of object material  112  relative to the surface of conducting element  28  are detected and used to generate error signals. The detection and generation of error signals may be by known techniques in the art such as cap gauges, precision distance measuring interferometry including wave domain reflectometry [see, e.g., commonly owned U.S. patent application with Ser. No. 09/089,105 and entitled “Methods And Apparatus For Confocal Interference Microscopy Using Wavenumber Domain Reflectometry And Backgroung Amplitude Reduction And Compensation” by Henry A. Hill, the contents of which are incorporated herein by reference], and scanning interferometric near-field microscopy [see, e.g., the previously mentioned provisional application entitled “Control of Position and Orientation of Sub-Wavelength Aperture Array in Near-field Scanning Microscopy” by Henry A. Hill.] 
     The error signals are transmitted as a component of signal  166  to electronic controller, signal processor, and computer  200 . Servo control signals are generated by electronic controller, signal processor, and computer  200  from the error signals and transmitted as a servo control signal component of signal  166  to chuck stage  162 . Transducers  161 A,  161 B, and the third transducer (not shown) alter the orientation and/or height of object material  112  according to the servo control signal component of signal  166 . 
     The location of chuck stage  162  in a plane substantially parallel to the surface of conducting element  28  is controlled by translator  164 . The location of chuck stage  162  is detected by known techniques in the art such as precision distance measuring interferometry and error signals transmitted as an error signal component of signal  168  to electronic controller, signal processor, and computer  200  [see U.S. patent application with Ser. No. 09/252,266 entitled “Interferometer And Method For Measuring The Refractive Index And Optical Path Length Effects Air” by Peter de Groot, Henry A. Hill, and Frank C. Demarest filed Feb. 18, 1999 and U.S. patent application with Ser. No. 09/252,266 entitled “Apparatus And Method For Measuring The Refractive Index And Optical Path Length Effects Of Air Using Multiple-Pass Interferometry” by Henry A. Hill, Peter de Groot, and Frank C. Demarest filed Feb. 18, 1999, the contents of both applications being incorporated herein by reference.] 
     Servo control signals are generated by electronic controller, signal processor, and computer  200  from the error signal component of signal  168  and transmitted as a servo signal component of signal  168  to translator  164 . Translator  164  controls the location and orientation of chuck stage  162  in one or two orthogonal directions and in one or two orthogonal planes of orientation, according to the requirements of an end-use application, in response to the servo signal component of signal  168 . 
     Next, the object material  112  is scanned in a combination of one or two orthogonal directions substantially parallel to the surface of object material  112  and in the spatial separation of the conducting element  28  and the adjacent surface of object material  112  according to the requirements of an end-use application. Measured arrays of signal values [S n ] 1 , [S n ] 2 , [S n ] 3 , and [S n ] 4  and, if required by an end-use application, measured arrays of signal values [S n ] 5 , [S n ] 6 , [S n ] 7 , and [S n ] 8  are obtained as a function of the scanned parameters and the amplitude and phase of the respective interference cross terms between the complex amplitude of the respective near field return probe beam and of the respective complex amplitude of the reflected reference beam computed by electronic controller, signal processor, and computer  200 . 
     Information with apparatus of the first embodiment about object material  112  is acquired in the presence of a significantly reduced background signal. Sources of contributions to the background signal comprise the first background return beam, the return measurement beam, a background produced by reflection and/or scattering of other beams associated with the measurement beam in the apparatus of the first embodiment, and corresponding beams associated with the reflected reference beam. The background signal is significantly reduced first because the apparatus of the first embodiment comprises a confocal optical imaging/detecting system and second because of the background compensation procedure based on measurement of the second background return beam. 
     The background compensation procedure based on measurement of the second background return beam compensates for the first background return beam that is not discriminated against by the confocal imaging/detecting properties of the apparatus of the first embodiment. It should be noted that The background compensation procedure based on measurement of the second background return beam further compensates for the scattered/reflected beams generated in plane sections displaced from the plane section being imaged not discriminated against by the confocal imaging/detecting properties of the apparatus of the first embodiment. 
     The scanning of object material  112  in a combination of one or two orthogonal directions substantially parallel to the surface of object material  112  and in the spatial separation of the conducting element  28  and the adjacent surface of object material  112  is implemented for the first embodiment as a “step and repeat” mode. The first embodiment modified for a continuous scan mode of operation is subsequently described as the third embodiment of the present invention. 
     The scanning of object material  112  in a combination of one or two orthogonal directions substantially parallel to the surface of object material  112  and in the spatial separation of the aperture array element  142  from the adjacent surface of object material  112  is implemented for the first embodiment as a “step and repeat” mode. The first embodiment modified for a continuous scanning mode of operation is subsequently described as the third embodiment of the present invention. 
     The electric fields generated by any multipole source located at wavelength or sub-wavelength apertures  30  and associated with the near field probe beams for the first, embodiment and variants thereof generally have restricted ranges in directions at a specific location in object material  112 . This feature of the present invention generally leads to a simpler inverse calculation for properties of the object material  112  from the measured arrays of signal values [S n ] 1 , [S n ] 2 , [S n ] 3 , and [S n ] 4  and, if required by an end-use application, measured arrays of intensity values [S n ] 3 −[S n ] 4 =[(S I ) n ] 3 −[(S I ) n ] 4  as compared to the inverse calculation encountered in profilers, interferometric or otherwise, which rely a spatial resolution defined by imaging with a traditional optical system. 
     The inverse calculation is simpler in the present invention because is the directions of propagation of components of a near-field probe beam at a given volume section of an object being profiled/imaged are substantially the same for a given measured amplitude and phase of a reflected/scattered near-field probe beam from the volume section wherein the dimensions of the volume section are much less than the dimensions of the source of the near-field probe beam. The inversion type of calculation is further simplified in the present invention because is the directions of propagation of components of a reflected/scattered near-field probe beam from a given volume section of an object being profiled/imaged are substantially the same for a given measured amplitude and phase of a reflected/scattered near-field probe beam from the volume section The inversion type of calculation is also further simplified in the present invention because the directions of propagation of components of a near-field probe beam at a given volume section of an object being profiled/imaged and the directions of propagation of components of a resulting reflected/scattered near-field probe beam from the volume section of the object being profiled/imaged are substantially in opposite directions for a given measured amplitude and phase of a reflected/scattered near-field probe beam from the volume section. 
     Optical cavity  130  under certain conditions is a stable resonant cavity excited by the beam incident on optical cavity  130 . Certain properties of particular interest with respect to the first embodiment are (1) a resonant condition that leads to excitation of optical cavity  130  by the beam incident on optical cavity  130  with a corresponding buildup of optical beam  107  in optical cavity  130 , (2) a condition for cavity stability for a given transverse mode, (3) a condition for exciting a stable transverse mode, and (4) a condition relating to the rate of compensation of optical cavity  130  for a perturbation of the wavefront of a stable transverse mode. Excitation of optical cavity  130  with the buildup of beam  107  inside optical cavity  130  reaches a maximum when
 
λ 1 =(2η 1   d   1   /p   1 )  (3)
 
where η 1  is the index of refraction of Amici type lens  132  for wavelength λ 1 , d 1  is the spacing between interfaces  124  and  143 , and p 1  is an integer. Beam  107  comprises a standing wave in optical cavity  130 . The intensity of beam  107 , when the resonant condition expressed by Eq. (3) is satisfied, is in general larger than the intensity of the beam incident on cavity  130  and determined in part by the effective reflectivities R 1  and R 2  of interfaces  124  and  143 , respectively.
 
     There are a variety of resonator configurations that can be used for optical cavity  130 . The use of slightly curved surfaces for interfaces  124  and/or  143  leads to much lower diffraction losses of a transverse mode than does a configuration wherein interfaces  124  and  143  are both planar surfaces, and the slightly curved surface configuration also has much less stringent alignment tolerances. 
     The preferred configuration of interface  143  is planar although the configuration of interface  143  could be curved according to an end-use application without departing from the scope or spirit of the instant invention. Accordingly, the preferred surface geometry for interface  124  is curved with a radius of r 1 . Interface  124  may, however, be planar without departing from the spirit or scope of the instant invention. With the radius of curvature of interface  143  being r 2 , the condition for a stable transverse mode is given by 
             0   &lt;       (     1   -       d   1       r   1         )     ⁢     (     1   -       d   1       r   2         )       &lt;   1.           (   4   )             
 
Thus, not all cavity configurations are stable with for example, the planar configuration, r 1 =r 2 =∞, and the hemispherical configuration, r 1 =d 1  and r 2 =∞, being just on the edge of stability.
 
     A stable mode comprises a beam in optical cavity  130  that results from a cavity configuration which concentrates the beam toward the resonator axis in a regular pattern as it traverses back and fourth within the cavity, rather than allowing it to diverge and escape from the resonator. Therefore when the resonant condition is satisfied, optical cavity  130  increases the component of intensity of beam  107  propagating towards and in the vicinity of wavelength/sub-wavelength apertures  30  and wavelength/sub-wavelength sites  32  over that intensity which would be obtained in the absence of optical cavity  130 . When the resonant condition is satisfied, the increase in intensity of the component of beam  107  at interface  124  propagating away from interface  124  is given to a good approximation for a non-absorbing cavity by 
                 T   1         [     1   -       (       R   1     ⁢     R   2       )       1   /   2         ]     2       ,           (   5   )             
 
T 1 =(1−R 1 ) for a non-absorbing interface, when (1) the radius of curvature of the wavefront of beam  107  at surface  122  is equal to the radius of curvature r 1 , (2) the widths of the beam incident on cavity  130  and of beam  107  at interface  124  are equal, and (3) the amplitude distribution of the beam incident on optical cavity  130  at interface  124  matches the amplitude distribution of the stable transverse mode of optical cavity  130  at interface  124 .
 
     The widths of the beam incident on optical cavity  130  and of beam  107  are equal at interface  124  when the width of the beam incident on optical cavity  130  at interface  124  matches the width of a stable transverse mode of optical cavity  130  and the amplitude distribution of the beam incident on optical cavity  130  at interface  124  matches the amplitude distribution of the stable transverse mode of optical cavity  130  at interface  124 . The preferred stable transverse mode for cavity  130  is a TEM 00  mode, i.e., a Gaussian mode. 
     An important property of an excited Gaussian mode is that the associated wavefront at interface  143  is uniphase when the resonant condition of Eq. (3) is satisfied. In addition, the associated wavefront at interface  143  is planar. 
     When the resonant condition of Eq. (3) is satisfied but the radius of curvature r 1  is not equal to the radius of curvature of the wavefront of beam  107  at interface  124 , the amplitude distribution of the resulting built-up beam in optical cavity  130  at interface  124  is different from the amplitude distribution of a stable mode and of the amplitude distribution of the beam incident on optical cavity  130 . 
     As a consequence, optical cavity  130  configured for meeting the resonant condition and the condition for a transverse mode to be excited by the beam incident on optical cavity  130 , an enhancement of optical transmission through wavelength/sub-wavelength apertures  30  is achieved over that transmission which would be obtained in the absence of optical cavity  130  by the ratio given by Eq. (5) multiplied by the square of the ratio of the diameter of the intercavity beam intensity at interface  124  to the corresponding diameter at interface  143 . As such supports enhanced transmission is achieved in the first embodiment of an optical beam through an array of wavelength/sub-wavelength apertures. 
     The maximum enhancement is obtained when the term given by Eq. (5) is a maximum. The term given in Eq. (5) is a maximum when reflectivity R 1  is chosen such that for a given value of R 2 ,
 
R 1 =R 2   (6)
 
and the enhancement is increased as reflectivity R 2  is increased towards the value of 1. It was assumed in deriving Eq. (6) that T 1 +R 1 =1.
 
     Beam  107  forms a waist with radius w 1  at interface  143 . The dimension 2w 1  is selected to be large enough to encompass a preselected portion of aperture-array element  142 . As is known in the art, the value of w 1  is related to the values of d 1  and r 1 . 
     Another condition on the system may be considered to enhance transmission of the optical beam through wavelength/sub-wavelength apertures  30 . That condition may be derived considering the angular width of beams back scattered or diffracted backwards at interface  143  as
 
λ 1 d 1 ≳η 1 ab  (7)
 
where a and b are lengths characteristic of the size and spacing, respectively, of wavelength/sub-wavelength apertures  30 . This condition will hereinafter be referenced as the redistribution condition.
 
     Thus when the redistribution condition expressed by Eq. (7) is met by optical cavity  130  and wavelength/sub-wavelength apertures  30  and beam  107  has the properties of a stable transverse mode for a case when wavelength/sub-wavelength apertures  30  and wavelength/sub-wavelength sites  32  are absent, a utilitarian redistribution of optical power in optical cavity  130  is achieved for the case when wavelength/sub-wavelength apertures  30  are present such that the spatial properties of beam  107  are substantially the same. As a further consequence of the spatial properties of beam  107  being substantially the same as the spatial properties of a stable transverse mode, the value for reflectivity R 2  is to a good approximation a weighted average of the reflectivity of the portion of interface  143  not occupied by wavelength/sub-wavelength apertures  30  and wavelength/sub-wavelength sites  32  and of the reflectivity of the wavelength/sub-wavelength apertures  30  and wavelength/sub-wavelength sites  32  for reflection of an optical beam back into the stable transverse mode excited in optical cavity  130 . 
     Wavelength λ 1  and/or the optical path length η 1 d 1  of optical cavity  130  are adjusted in the first embodiment so that the resonant condition expressed by Eq. (3) is satisfied. Wavelength λ 1  of source  10  may be adjusted for example by changing the injection current of a source comprising a diode laser or by changing the length of the cavity of a source  10  comprising a laser. The optical path length η 1 d 1  of optical cavity  130  is adjusted by changing the temperature of the element  132 . 
     A measured reflectivity of optical cavity  130  is used to generate a servo control signal  154  for the control of either λ 1 , if not controlled by servo control signal  186 R derived from reflection properties of the reference optical cavity, and/or the optical path length η 1 d 1  of optical cavity  130  through control of the temperature of cavity  130  so that the resonant condition expressed by Eq. (3) is satisfied. Servo control signal  154  is shown in  FIG. 1  for the control of the wavelength of source  10 . A portion of the beam incident on optical cavity  130  is reflected back to non-polarizing beam splitter  104 , after reflection by mirror  112 A, where a portion thereof is transmitted by non-polarizing beam splitter  104  as beam  109 . 
     Beam  109  is detected by detector  150 , preferably by a quantum photon detector [see Section 15.3 in Chapter 15 entitled “Quantum Detectors”,  Handbook of Optics,  1, 1995 (McGraw-Hill, New York) by P. R. Norton], as electrical signal  152 . Signal  152  is transmitted to electrical controller, signal processor, and computer  200  to generate servo control signal  154 . The reflectivity R C1  of optical cavity  130  at interface  124  is given by the formula 
               R   C1     =     1   -         T   1     ⁢     T   2             [     1   -       (       R   1     ⁢     R   2       )       1   /   2         ]     2     +     4   ⁢       (       R   1     ⁢     R   2       )       1   /   2       ⁢       sin   2     ⁡     (       δ   1     /   2     )                       (   8   )             
 
where
 
δ 1 =2k 1 η 1 d 1 ,  (9) 
 
T 2 =(1−R 2 ) for a non-absorbing interface, and wavenumber k 1 =2π/λ 1 .
 
     For generation of control signal  154 , wavenumber k 1  is modulated by a small amount at angular frequency ω 1  so as to amplitude modulate phase δ 1  with an amplitude Δδ 1 . The error signal upon which control signal  154  is based comprises the amplitude and phase of the first harmonic at angular frequency ω 1  of signal  152 . The amplitude and phase of the first harmonic is obtained using heterodyne techniques well known to those skilled in the art. The amplitude of the first harmonic is zero when resonant condition expressed by Eq. (3) is satisfied. 
     A deviation of phase δ 1  from the value of 2πp 1  will introduce a corresponding phase shift Φ 1  between the phase of beam  146  transmitted by aperture-array element  142  relative to the phase of beam  24 . In certain end-use applications, knowledge of phase shift Φ 1  is not required. In other end-use applications wherein enhanced transmission through an array of apertures to produce a source comprising an array of wavelength or sub-wavelength sources in one or more locations, such as in an interferometric microscopy tool, knowledge of phase shift Φ 1  may be required. 
     For those applications wherein a portion of a beam corresponding to beam  146  can not be split off by a beam splitter, e.g., due to spatial restrictions such as encountered with beam  146  of the first embodiment or the properties of arrays of signal values [S n ] are not available for a determination phase shift Φ 1 , phase shift Φ 1  can be measured and monitored by measuring and monitoring properties of the beam reflected by optical cavity  130 . From the measurement of the reflectivity R C1  of optical cavity  130 , the optical path length δ 1  can be determined using Eq. (8) with independent determinations of R 1  and R 2 . The independent determinations of R 1  and R 2  are preferably based on measured behavior of reflectivity R C1  of cavity  130  as δ 1  is varied. Phase shift Φ 1  is related to optical path length δ 1  to a good approximation as 
               Φ   1     =       tan     -   1       ⁢           ⁢             (       R   1     ⁢     R   2       )       1   /   2       ⁢   sin   ⁢           ⁢     δ   1         [     1   -         (       R   1     ⁢     R   2       )       1   /   2       ⁢   cos   ⁢           ⁢     δ   1         ]       .               (   10   )             
 
Thus, phase shift Φ 1  of beam  146  resulting from the enhanced transmission by aperture-array element  142  can be determined by measuring and monitoring reflectivity R C1  and using Eq. (10) for a calculation of a corresponding Φ 1 .
 
     An important property of optical cavity  130  is a relatively short time for build up and/or decay of a transverse mode. The 1/e time constant τ 1  for the build-up or decay time of intensity in optical cavity  130  is given by the equation 
               τ   1     ≅       (       2   ⁢     η   1     ⁢     d   1       c     )     ⁢     1     (       T   1     +     T   2       )                 (   11   )             
 
where c is the free space speed of light. For a non-limiting example of d 1 =2.5 mm, optical cavity  130  comprising gallium phosphide with η 1 =3.3 at λ 1 =630 nm, and R 1 =R 2 =0.99,
 
τ 1 ≅2.8 nsec.  (12)
 
     Another important consideration is the pulse width τ p1  for embodiments wherein a source corresponding to source  10  is a pulsed source, e.g., in a scanning near-field microscope. For enhanced transmission through aperture-array element  142  to be substantially the same when using a pulsed source in a scanning mode and when operating with a non-pulsed source in a non-scanning mode, there is a restriction on pulse width τ p1 . The restriction on pulse width τ p1  is determined by consideration of the width in frequency of beam  24  comprising a pulsed beam and the full width at half maximum in frequency of the enhanced transmission through aperture-array element  142 . 
     The full width at half maximum in frequency Δv 1/2  of beam  24  is 
               Δ   ⁢           ⁢     v     1   /   2         =       1     τ   p1       .             (   13   )             
 
The full width at half maximum in frequency Δv C1  of the enhanced transmission through aperture-array element  142  is obtained from the free spectral range c/(2η 1 d   1 ) and finesse F 1  of optical cavity  130 . Finesse F 1  is given by the formula 
                 F   1     =     π   ⁢           ⁢         (       R   1     ⁢     R   2       )       1   /   4         1   -       (       R   1     ⁢     R   2       )       1   /   2               ⁢     
     ⁢   with           (   14   )                 Δ   ⁢           ⁢     v   C1       =       1   π     ⁢     (     c     2   ⁢     η   1     ⁢     d   1         )     ⁢       (       1   -       (       R   1     ⁢     R   2       )       1   /   2             (       R   1     ⁢     R   2       )       1   /   4         )     .               (   15   )             
 
Note that 
               Δ   ⁢           ⁢     v   C1       ≅       1     2   ⁢     πτ   1         .             (   16   )             
 
     The restriction on pulse width τ p1  is based on a requirement that
 
Δv 1/2 &lt;Δv C1   (17)
 
or on combining Eqs. (13), (16), and (17),
 
τ p1 &gt;2πτ 1 .  (18)
 
Accordingly, on combining Eqs. (11) and (18), 
               τ   p1     &gt;       π   ⁡     (       2   ⁢     η   1     ⁢     d   1       c     )       ⁢       (         (       R   1     ⁢     R   2       )       1   /   4         1   -       (       R   1     ⁢     R   2       )       1   /   2           )     .               (   19   )             
 
     For a non-limiting example of d 1 =2.5 mm, optical cavity  130  comprising gallium phosphide with η 1 =3.3 at λ 1 =630 nm, and R 1 =R 2 =0.99, the restriction pulse width τ p1  expressed by Eq. (19) is
 
τ p1 &gt;17 nsec.  (20)
 
     As a consequence of the inequality expressed by Eq. (18), pulse width τ p1  will be a parameter that in part controls the limiting value for spatial resolution in the direction of a scan to
 
τ p1 v  (21)
 
where v is the scan speed. For example, with a value of τ p1 =50 nsec, a scan speed of v=0.20 m/sec, the τ p1  associated limiting spatial resolution in the direction of scan will be
 
τ p1 v=10 nm.  (22)
 
     Thus, the use of an optical cavity in the first embodiment to generate enhanced transmissions through an array of wavelength and/or sub-wavelength apertures is compatible with both the wavelength and sub-wavelength spatial resolution requirements of a scanning near-field microscope and the requirement for obtaining a high spatial resolution profile of a surface of a sample in a relatively short period of time. 
     It will be evident to those skilled in the art that transverse modes other than the TEM 00  may be used without departing from either the scope or spirit of the instant invention. The other transverse modes would be excited by beam  24  at an appropriate angle of incidence at optical cavity  130  and by the wavefront of beam  24  having a set of appropriate spatial properties at optical cavity  130 . The use of transverse modes other than the TEM 00  in optical cavity  130  permits operation wherein enhanced transmission through apertures  30  is achieved with differing amplitudes and phases according to a preselected pattern across aperture-array element  142 . 
     It will be further evident to those skilled in the art that an enhanced transmission through wavelength/sub-wavelength apertures  30  that is less than the maximum described herein can also be achieved with a relaxation to varying degrees of one or more of the conditions cited for excitation of a transverse mode of a stable resonant cavity by the beam incident on optical cavity  130  without departing from either the scope or spirit of the instant invention. 
     A measured reflectivity of the reference optical cavity is used to generate a servo control signal  186 R for the control of either λ 1 , if not controlled by servo control signal  154  derived from reflection properties of optical cavity  130 , and/or the optical path length η 1R d 1R  [see  FIG. 2   c ] of the reference optical cavity so that the resonant condition expressed by Eq. (3) is satisfied. The optical path length η 1R d 1R  would be controlled through control of the temperature of reference object  130 R. Description of the generation of servo control signal  186 R is the same as corresponding portions of the description for the generation of servo control signal  154  through detection of reflected light from the reference cavity to the detector  150 R. 
     Alternatively, servo control signal  186 R may be generated from measured values of enhanced transmission of the reference optical cavity. A portion of transmitted reference beam  56  is split off by a non-polarizing beam splitter and detected, preferably by a quantum photon detector, to generate an electronic signal corresponding to  152 R (the non-polarizing beam splitter, the detector, and the signal corresponding to  152 R are not shown in a figure). The signal corresponding to  152 R is transmitted to electronic controller, signal processor, and computer  200  to generate a servo control signal corresponding to  186 R. 
     The transmission T C1  of the reference optical cavity, as represented by the magnitude of the signal corresponding to  152 R, is given by the formula 
               T   C1     =           T   1     ⁢     T   2             [     1   -       (       R   1     ⁢     R   2       )       1   /   2         ]     2     +     4   ⁢       (       R   1     ⁢     R   2       )       1   /   2       ⁢       sin   2     ⁡     (       δ   1     /   2     )             .             (   23   )             
 
Generation of the control signal corresponding to  186 R uses the modulation of wavenumber k 1  introduced for the generation of servo control signal  154  to modulate T C1 . The error signal upon which the control signal corresponding to  186 R is based comprises the amplitude and phase of the first harmonic at angular frequency ω 1  of the signal corresponding to  152 R. The amplitude and phase of the first harmonic is obtained using heterodyne techniques well known to those skilled in the art. The amplitude of the first harmonic is zero when resonant condition expressed by Eq. (3) is satisfied.
 
     A phase shift Φ 1  for transmitted reference beam  56  can be measured and monitored by measuring and monitoring properties of transmitted reference beam  56 . From measurement of the T C1 , the corresponding optical path length δ 1  can be determined using Eq. (23) with independent determinations of corresponding R 1  and R 2 . The independent determinations of corresponding R 1  and R 2  are preferably based on measured behavior of reflectivity T C1  as corresponding δ 1  is varied. Phase shift Φ 1  for transmitted reference beam  56  is then determined from the measured value for corresponding δ 1  using an equating corresponding to Eq. (10). 
     An advantage of the alternative procedure for generation of the servo control signal control signal  186 R is the acquisition of information directly from properties of the enhanced transmission by aperture-array element  142 R for the control of either λ 1 , if not controlled by servo control signal  154  derived from reflection properties of the optical cavity  130 , and/or the reference optical cavity instead of the acquisition of information from reflective properties of the reference optical cavity as already described. 
     A first variant of the first embodiment is disclosed wherein the control of optical path lengths in optical cavities is achieved by changing the physical lengths of the respective optical cavities. Description of the first variant of the first embodiment is the same as corresponding portions of the first embodiment except with respect to the control of optical path lengths of optical cavities of the first variant of the first embodiment. Optical cavity  130  of the first variant of the first embodiment is shown schematically in  FIG. 2   f  and is defined by surface  124  of lens  122  and interface  143 . Surface  124  has a high reflective coating with reflectivity R 1  and surface  123  is antireflection coated for wavelength λ 1 . The axial position of lens  122  is controlled by transducers  162 A and  162 B. 
     Cavity  130  comprises element  132 , having an index of refraction η 1 , and the space between element  132  and lens  122 . Surface  133  is antireflection coated for wavelength λ 1 . The space between element  132  and lens  122  is preferably occupied by a gas or a vacuum. However, for certain end-use applications, the space may be partially filled with an optical medium for the purposes of making for example the optical path of optical cavity  130  achromatic. 
     The radii of curvature of surfaces  124  and  133  are selected so that a condition for existence of a stable transverse mode for the first variant of the first embodiment, corresponding to Eq. (4) for the first embodiment, is satisfied. 
     The optical path length of the optical cavity  130  of the first variant of the first embodiment that corresponds to the optical path length η 1 d 1  of cavity  130  of the first embodiment is
 
η 1 d 1 +d 2 .  (24)
 
     The measured reflectivity of cavity  130  of the first variant of the first embodiment is used to generate a servo control signal  186  for control of optical path length η 1 d 1 +d 2  so that the resonant condition corresponding to that expressed by Eq. (3) is satisfied. The description of the generation of servo control signal  186  for the first variant of the first embodiment is the same as corresponding portions of the description given for the generation of servo control signal  154  of the first embodiment. Optical path length η 1 d 1 +d 2  is controlled through the change in d 2  by transducers  162 A and  162 B which are controlled in turn by servo control signal  186 . 
     The reference optical cavity of the first variant of the first embodiment is shown schematically in  FIG. 2   g  and is defined by surface  124 R of lens  122 R and interface  143 R. Surface  124 R has a high reflective coating with reflectivity R 1  and surfaces  123 R and  133 R are antireflection coated for wavelength λ 1 . The axial position of lens  122 R is controlled by transducers  162 RA and  162 RB. The remaining description of the control of the reference optical cavity of the first variant of the first embodiment is the same as corresponding portions of the descriptions given for the control of the reference optical cavity of the first embodiment and of optical cavity  130  of the first variant of the first embodiment. 
     An advantage of the first variant of the first embodiment is that the properties of asociated optical cavities are controlled through changes in the physical lengths of the respective optical cavities so as to meet the respective resonant conditions corresponding to that expressed by Eq. (3) instead of the changing the wavenumber k 1  and/or optical paths lengths as in the first embodiment. 
     The remaining description of the first variant of the first embodiment is the same as corresponding portions of the description given for the first embodiment. 
     It will be evident to those skilled in the art that spacings d 2  and d 2R  may be modulated by transducers  162 A and  162 B and transducers  162 RA and  162 RB, respectively in lieu of a modulation of wavenumber k 1  to achieve the amplitude modulation of respective phases δ 1  at angular frequency ω 1  without departing from the scope or spirit of the present invention. A modulation of spacings d 2  and d 2R  has an advantage that wavenumber k 1  is not modulated in beams  146  and  146 R, the beam resulting from enhanced transmission through aperture-array elements  142  and  142 R, respectively. 
     Referring to the drawings,  FIG. 3  illustrates, in schematic form, the second embodiment of the present invention. The second embodiment comprises a scanning interferometric near-field confocal microscope operating in a reflection mode with enhanced transmission of an optical beams through arrays of wavelength or sub-wavelength apertures. The second embodiment further incorporates interferometric techniques to measure and monitor properties of optical cavities whereas the first embodiment and variants thereof use non-interferometric techniques. Interferometric techniques offer advantages in increased signal-to-noise ratios, direct measurements of relative phases between optical beams, and the measurement of the properties of the optical cavities without the requirement of altering either the frequency of an optical beam and/or properties of the optical cavities. 
     The second embodiment comprises many elements performing like functions as elements of the first embodiment. Elements in  FIG. 3  with element numbers the same as element numbers in  FIG. 1   a  are corresponding elements and perform substantially the same functions as the corresponding elements of the first embodiment. 
     Description of the second embodiment is the same as corresponding portions of the first embodiment except with respect to generation of servo control signals for control of optical path lengths of optical cavity  130  and of the reference optical cavity. For generation of a servo control signal from properties of optical cavity  130 , a portion of the beam incident on optical cavity  130  is reflected back to non-polarizing beam splitter  104 , after reflection by mirror  112 A, where a portion thereof is transmitted by non-polarizing beam splitter  104  as a measurement beam component of beam  109 . 
     A second portion of beam  22  is transmitted by non-polarizing beam splitter  104  as an optical cavity  130  reference beam. The optical cavity  130  reference beam is reflected by mirror  74  as a reflected optical cavity  130  reference beam back to beam splitter  104  where a portion thereof is reflected as a reference beam component of beam  109 . The plane of polarization of the measurement and reference beam components of beam  109  is parallel to the plane of FIG.  3 . 
     The reference beam component of beam  109  makes a double pass through phase shifter  72  wherein a double pass phase shift χ 2  is introduced. Phase shift χ 2  is controlled by electronic signal  166  from electroniccontroller, signal processor, and computer  400 . 
     The complex reflectivity coefficient R C2  for optical cavity  130  is given to a good approximation for a non-absorbing cavity by the equation 
                   (     R     C   ⁢           ⁢   2       )       1   /   2       =       R   3     1   /   2       -       T   3     ⁢       {       R   4           (     [     1   -       (       R   3     ⁢     R   4       )       1   /   2         ]     )     2     +     4   ⁢       (       R   3     ⁢     R   4       )       1   /   2       ⁢       sin   2     ⁡     (       δ   2     /   2     )             }       1   /   2       ⁢     ⅇ     ⅈ   ⁡     (       δ   2     +     Φ   2       )               ⁢     
     ⁢   where           (   25   )                   Φ   2     =       tan       -   1     ⁢               ⁢           ⁢           (       R   3     ⁢     R   4       )       1   /   2       ⁢   sin   ⁢           ⁢     δ   2         [     1   -         (       R   3     ⁢     R   4       )       1   /   2       ⁢   cos   ⁢           ⁢     δ   2         ]           ,           (   26   )             
 
i=√{square root over ((−1))}, and reflectivities R 3  and R 4  and transmission coefficients T 3  and T 4  of the second embodiment correspond to reflectivities R 1  and R 2  and transmission coefficients T 1  and T 2 , respectively, of the first embodiment. Phase δ 2  is given by an equation corresponding to Eq. (9) with the wavenumber k 1  replaced by k 2  of the second embodiment.
 
     Beam  109  is detected by detector  150 , preferably by a quantum photon detector, to generate electrical interference signal  152  or signal s 2 . Signal s 2  can be written to a good approximation as
 
 s   2   =A   2   |R   C2 | 1/2  cos(Φ 2 +χ 2 +ζ 2 )  (27)
 
where ζ 2  is a phase that is not a function of either Φ 2  or χ 2 , and A 2  is a proportionality constant dependent on the magnitude of the amplitude of the reference beam component of beam  109 .
 
     Electronic controller, signal processor, and computer  400  determines phase (Φ 2 +ζ 2 ) of signal s 2  by measuring s 2  for a set of values of χ 2 . The set of values of χ 2 , e.g., 0, π/2, (3/2)π, and π, are controlled by electronic controller, signal processor, and computer  400  through signal  166 . A measured value of s 2  for a given value of χ 2  from the set of values of χ 2  preferably corresponds to one or more pulses of source  10 . 
     The value of Φ 2  is determined from the measured phase (Φ 2 +ζ 2 ) by subtracting a value for ζ 2  independently determined. 
     An independent determination of ζ 2  can be made by measuring both (Φ 2 +ζ 2 ) and amplitude A 2 |R C2 | 1/2  of s 2  as functions of wavenumber k 2 . Amplitude A 2 |R C2 | 1/2  exhibits a minimum value when Φ 2 =0 [see Eq. (25)]. Therefore, the measured value of (Φ 2 +ζ 2 ) at the minimum value in A 2 |R C2 | 1/2  corresponds to an independent determination for ζ 2 . 
     Electronic controller, signal processor, and computer  400  uses the measured value of Φ 2  as an error signal to generate servo control signal  154 . Phase Φ 2  is an antisymmetric function of phase δ 2  about Φ 2 =0 [see Eq. (26)]. Servo control signal  154  is transmitted to source  10  to control the wavelength of beam  16  if not controlled by a signal corresponding control signal  186 R or the optical path length of optical cavity  130  by control of optical cavity temperature by  186  so that the condition Φ 2 =0 is maintained and therefore the resonant condition for cavity  130  is satisfied. 
     The condition Φ 2 =0 will be met only to a certain accuracy by the servo control of the wavelength of beam  16  or the optical path length of optical cavity  130 . The effects of the certain accuracy in down stream applications may be compensated in the second embodiment using measured values of phase shift Φ 2 . 
     The description of the generation of the servo control signal  186 R for the reference optical cavity of the second embodiment is the same as corresponding portions of the description given for the generation of servo control signal  186  of the second embodiment. 
     The remaining description of the second embodiment is the same as corresponding portions of the description given for the first embodiment and variant thereof of the present invention. 
     Advantages of the second embodiment are the generation by interferometric techniques the servo control signals for the optical cavities of the second embodiment leading to increased signal-to-noise ratios, direct measurements of a relative phases between optical beams, and the measurement of the properties of the optical cavities without the requirement of altering either the frequency of the optical beam and/or properties of the optical cavities. 
     An alternative procedure to that used in the second embodiment for the generation of servo control signals  154  and/or  186 , and  186 R is based on a modulation of χ 2  and χ 2R . Phase (Φ 2 +ζ 2 ) is determined using known heterodyne detection techniques or phase sensitive detection techniques for non-pulsed signals such as a digital Hilbert transform phase detector [see “Phase-locked loops: theory, design, and applications” 2nd ed. (McGraw-Hill, New York) 1993, by R. E. Best], a phase-locked loop [see R. E. Best, ibid.], a sliding window FFT [see  Digital Techniques for Wideband Receivers , (Artech House, Boston) 1995, by J. Tsui using phase χ as the reference phase. 
     It is known for a function sampled uniformly in time that an implementation of a phase sensitive technique based on digital signal processing for acquisition of information on the function yields results based on a Chebyshev polynomial representation of the function [see H. A. Hill and R. T. Stebbins,  Astrophys, J.,  200, p 484 (1975)]. Consider the example of phase χ 2  being scanned about an offset χ 2,0  so that
 
χ 2 =χ 2,0 =Δχ 2   (28)
 
where Δχ 2  is some function of time t.
 
     The scanning of χ 2  generates components according to the Eqs. (27) and (28) expressed as
 
 s   2   =A   2   |R   C2 | 1/2  cos(Φ 2 +ζ 2 )cos Δχ− A   2   |R   C2 | 1/2  sin(Φ 2 +ζ 2 )sin Δχ.  (29)
 
The amplitude A 2 |R C2 | 1/2   and phase (Φ 2 +ζ 2 ) are then obtained by way of phase sensitive detection of the coefficients of cos Δχ and sin Δχ. The phase sensitive detection comprises multiplying s 2  by cos Δχ and integrating s 2  cos Δχ with respect to time and multiplying s 2  by sin Δχ and integrating s 2  sin Δχ with respect to time. For the case of Δχ being a sinusoidal function at an angular frequency ω 1  with an amplitude 1, i.e.,
 
Δχ 2 =cos ω 2 t,  (30)
 
and s 2  sampled uniformly in time, the coefficients of cos Δχ and sin Δχ can be expressed effectively as certain Chebyshev polynomial coefficients of s 2 .
 
     The certain Chebyshev polynomial coefficients can be expressed using known properties of Chebyshev polynomial as 
                       A   2     ⁢            R     C   ⁢           ⁢   2              1   /   2       ⁢     cos   ⁡     (       Φ   2     +     χ     2   ,   0         )         =       4     T   ⁡     [     1   +       J   0     ⁡     (   2   )         ]         ⁢       ∫       -   T     /   2       T   /   2       ⁢       s   2     ⁢   cos   ⁢           ⁢   Δχ   ⁢           ⁢     ⅆ   t                         =       4     [     1   +       J   0     ⁡     (   2   )         ]       ⁢       ∫     -   1     1     ⁢       s   2     ⁢         T   1     ⁡     (     Δχ   2     )           (     [     1   -       (     Δχ   2     )     2       ]     )       1   /   2         ⁢           ⁢     ⅆ     Δχ   2               ,                 (   31   )                         A   2     ⁢            R     C   ⁢           ⁢   2              1   /   2       ⁢     sin   ⁡     (       Φ   2     +     χ     2   ,   0         )         =       -     4     T   ⁡     [     1   -       J   0     ⁡     (   2   )         ]           ⁢       ∫       -   T     /   2       T   /   2       ⁢       s   2     ⁢   sin   ⁢           ⁢   Δχ   ⁢           ⁢     ⅆ   t                       =       -     4     [     1   -       J   0     ⁡     (   2   )         ]         ⁢       ∫     -   1     1     ⁢       s   2     ⁢         V   1     ⁡     (     Δχ   2     )           (     [     1   -       (     Δχ   2     )     2       ]     )       1   /   2         ⁢           ⁢     ⅆ     Δχ   2                           (   32   )             
 
where T=2π/ω 2 , T 1  and V 1  are order 1 Chebyshev polynomials of type I and type II, respectively, and J 0  is the order 0 Bessel function of the first kind [see Section 13.3 of  Mathematical Methods for Physicists  by G. Arfken (Academic Press-New York) 1968].
 
     Phase offset χ 2,0  can be determined for example by acquiring arrays of amplitudes [(|S 1 |) n ] and phases [(φ) n ] in array [S n ] for object material  112  comprising an isotropic medium, e.g., fused silica, with a surface flat to requisite accuracy, as a function of χ 2  and finding that value of χ 2 , χ 2,max , for which [(|S I |) n ] is a maximum. Phase offset χ 2,0  will correspond to −χ 2,max . 
     The description of the generation of servo control signal  186 R for the alternative procedure is the same as the description given for the determination of servo control signals  154  or  186  for the alternative procedure. 
     It will be evident to those skilled in the art that there is a variant to the second embodiment that corresponds to the first variant of the first embodiment. 
     Referring to the drawings,  FIG. 4  illustrates, in schematic form, the third embodiment of the present invention. The third embodiment comprises a pulsed source, generates enhanced transmission of an optical beam through an array of wavelength and/or sub-wavelength apertures, and incorporates interferometric techniques to measure and monitor properties of optical cavities. The pulsed source enables the operation of a near-field interferometric confocal microscope in a continuous scanning mode. Interferometric techniques offer advantages in increased signal-to-noise ratios, direct measurements of a relative phases between optical beams, and the measurement of the properties of optical cavities without the requirement of altering either the frequency of the optical beam and/or properties of the optical cavities. 
     The third embodiment comprises many elements performing like functions as elements of the second embodiment. Elements in  FIG. 4  with element numbers the same as element numbers of certain elements in  FIG. 3  are corresponding elements and perform the same functions as the corresponding elements of the second embodiment. 
     Source  1010  is a pulsed source generated by one of a number of different ways for producing a pulsed source (Silfvast, op. cit.). Source  1010  produces optical beam  1016  that is plane polarized in the plane of FIG.  3 . Beam  1016  is incident on a modulator  76  and exits modulator  76  as beam  1018 . Modulator  76  is excited by a driver  78 . Modulator  76  may for example be an acousto-optical device or a combination of acousto-optical devices with additional optics for modulating a portion of beam  1016 . Modulator  76  diffracts by an acousto-optical interaction a portion of beam  1016  as a diffracted beam component of beam  1018 . The oscillation frequency of the diffracted beam component of beam  1018  is frequency shifted by an amount f 3  with respect to the non-diffracted, non-frequency shifted component of beam  1018  and is linearly polarized orthogonal to the plane of FIG.  4 . 
     The plane of polarization of the non-frequency shifted component of beam  1018  is parallel to the plane of FIG.  4 . The diffracted component of beam  1018  is reflected by polarizing beam splitter  302  and then transmitted by phase retardation plate  18  as a measurement beam  1022 . The non-diffracted component of beam  1018  is transmitted by polarizing beam splitter  302  and then transmitted by phase retardation plate  18 R as a measurement beam  1052 . The descriptions of the remaining beams which are pulsed are otherwise the same as the descriptions given for corresponding portions of the description of the second embodiment. 
     Beam  40  is detected by detector  116 , preferably by a quantum photon detector, to generate electrical interference signal  1031  comprising an array of signal values [S n ]. Array of signal values [S n ] can be written to a good approximation the same as Eq. (1) wherein
 
( S   I ) n =(| S   I |cos(ω 3   t+φ+χ+ζ   3 )) n ,  (33)
 
ω 3 =2πf 3  and ζ 3  is a phase that is not a function of either φ, χ, or t.
 
     Electronic controller, signal processor, and computer  600  determines phase (φ+χ+ζ 3 ) of (S I ) n  by either digital or analog signal processes, preferably digital processes, using time-based phase detection and the phase of driver  78  which is transmitted to electronic controller, signal processor, and computer  600  by signal  77 . The array of values of [(φ) n ] is determined from the measured array of phases [(φ+χ+ζ 3 ) n ] by subtracting array of phases [(χ+ζ 3 ) n ] independently determined if required in an end-use application. 
     The array of phases [(χ+ζ 3 ) n ] generally need not be determined other than meet the condition that it not be variable during a period of scanning object material  112 . To compare results obtained at different times, it may be necessary to determine any change in the array of phases [(χ+ζ 3 ) n ] that may have occurred during the time between the two different measurement periods. Relative changes in [(χ+ζ 3 ) n ] can be determined for example by acquiring arrays of signal values [S n ] for object material  112  comprising an isotropic medium, e.g., fused silica, with a surface flat to required accuracy. 
     The coherence time τ c  for a pulse of beam  1016  is substantially equal to the pulse width τ p3 . For the conditions where arrays of signal values [S n ] are measured by detector  116  as an integral over a time interval Δt, Δt&lt;&lt;τ c , and τ c &lt;&lt;1/f 3 , the description of signal values [S n ] is substantially the same as corresponding portions of the description given of arrays of signal values [S n ] of the first embodiment with χ of the first embodiment given by
 
χ=ω 3 t , modulo 2π.  (34)
 
     Therefore, the description of the third embodiment, when source  1010  is a pulsed source with a pulse coherence time of τ c , is equivalent to the description of the second embodiment with χ of the second embodiment replaced by ω 3 t, modulo 2π. The time of the pulses of source  1010  would be selected such ω 3 t comprise a set of values where each value of the set is an integer number of 2π plus a value from a finite set of values, e.g., 0, π/2, π, and (3/2)π. The timing of the pulses of source  1010  is controlled by signal  254  generated by electronic controller, signal processor, and computer  600 . 
     An advantage of the third embodiment with respect to the second embodiment is the frequency at which the phase corresponding to χ of the second embodiment can be changed. The frequency for the change in phase modulo 2π in the third, a phase equivalent to χ in the second embodiment, can be as high as of the order of 5 Mhz and remain consistent with the condition τ c &lt;&lt;1/f 3 . 
     The timing of pulses from source  1010  is coordinated by electronic controller, signal processor, and computer  600  so that for a scan speed v and the spacing of elements  30  and  32  of element  142 , information equivalent to arrays of signal values [S n ] 1 , [S n ] 2 , [S n ] 3 , and [S n ] 4  of the second embodiment is acquired for the third embodiment. A normalization is performed by electronic controller, signal processor, and computer  600  to compensate for a variation in efficiencies in generation and detection of interference cross terms between complex amplitudes of the near-field return probe beam or the amplitudes of the second background return beam and the reflected reference beam from one element to a second element of an array of signal values. Information required for the normalization can be determined for example by acquiring arrays of signal values [S n ] for object material  112  comprising an isotropic medium, e.g., fused silica, with a surface flat to required accuracy. 
     Phase shifter  64  may be used in the third embodiment to confirm that the values of phase shifts produced by the combination of the timing of the pulses from source  1010  and modulator  76  are equivalent to a desired set of phase shifts. 
     It will be evident to those skilled in the art that source  1010  of the third variant of the first embodiment may be replaced with a CW source and the phases of arrays of signal values [S n ] determined using known heterodyne detection techniques or phase sensitive detection techniques for non-pulsed signals such as a digital Hilbert transform phase detector [see “Phase-locked loops: theory, design, and applications” 2nd ed. (McGraw-Hill, New York) 1993, by R. E. Best], a phase-locked loop [see R. E. Best, ibid.], a sliding window FFT [see  Digital Techniques for Wideband Receivers , (Artech House, Boston) 1995, by J. Tsui], without departing from either the scope or spirit of the present invention. 
     It will also be evident to those skilled in the art that the third embodiment can be modified so as to obtain two or more simultaneous measurements of arrays of signal values [S n ] according to the teachings of the second variant of the first embodiment of previously mentioned U.S. Provisional Aplication entitled “Scanning Interferometric Near-Field Confocal Microscopy” by Henry A. Hill filed Jul. 27, 2000, without departing from the spirit and scope of the present invention. 
     Certain additional reflection and/or scattering properties of object material  112  are obtained by a fourth and fifth embodiments of the present invention wherein near-field probe beams are used that are different from the near-field probe beams used in the first, second, and third embodiments and variants thereof. The primary difference between the fourth and fifth embodiments and the first, second, and third embodiments and variants thereof is the angle of incidence of a measurement beam at the surface of aperture-array element  142 . For the first, second, and third embodiments and variants thereof, the angle of incidence is substantially normal to the surface of aperture-array element  142 . For the fourth and fifth embodiments, the corresponding angle of incidence is of the order of one radian as shown in  FIGS. 5 and 7 , respectively. 
     Referring to the drawings,  FIG. 5  illustrates, in schematic form, the fourth embodiment of the present invention. The fourth embodiment generates enhanced transmission of an optical beam through an array of wavelength and/or sub-wavelength apertures with a pulsed source. The fourth embodiment further incorporates interferometric techniques to measure and monitor properties of optical cavities. Interferometric techniques offer advantages in increased signal-to-noise ratios, direct measurements of relative phases between optical beams, and the measurement of the properties of the optical cavities without the requirement of altering either the frequency of an optical beam and/or properties of the optical cavities. 
     The fourth embodiment comprises many elements performing like functions as elements of the third embodiment. Elements in  FIG. 5  with element numbers the same as element numbers of certain elements in  FIG. 4  are corresponding elements and perform similar functions as the corresponding elements of the third embodiment. 
     The optical cavity of the fourth embodiment generally indicated at element number  230  in  FIG. 5  is illustrated schematically in expanded form in  FIG. 6   a . Optical cavity  230  is a ring cavity comprising mirrors  226 A and  226 B, Amici type lens  232 , and lenses  222 A and  222 B. Surfaces  227 A,  227 B,  223 B,  225 B,  233 B,  233 A,  224 A, and  223 A are antireflection coated for the wavelength of beam  1022 . Surfaces  228 A and  228 B have coatings with a high reflectivity. Interface  243  preferably has a high reflectivity. The description of aperture array element  242  is the same as the corresponding portion of the description given for aperture array element  142  of the first embodiment. 
     The resonant cavity of optical cavity  230  is defined by surfaces  228 A and  228 B and interface  243 . The general description of properties of optical cavity  230  is the same as corresponding portions of the description given for optical cavity  130  of the first embodiment. 
     As shown in  FIG. 5 , beam  1022  is incident on non-polarizing beam splitter  104  and a portion thereof is transmitted and then reflected by mirror  112 A as beam  24 . Beam  24  is transmitted by surface  227 A and incident on surface  228 A (see  FIG. 6   a ). The beam incident on surface  228 A excites optical cavity  230  with the build up of beam  207  when resonant conditions corresponding to Eq. (3) of the first embodiment are satisfied. 
     The focal lengths of lenses  222 A and  222 B are selected so that modes of optical cavity  230  are stable. The focal length of element  226 A is selected so that a stable transverse mode of optical cavity  330  is excited the beam incident on surface  228 A. The position and angular orientation of mirror  226 A is controlled by three transducers  162 A and  162 B (the third transducer is not shown in  FIG. 6   a ) and the position and angular orientation of mirror  226 B is controlled by three transducers  162 C and  162 D (the third transducer is not shown in  FIG. 6   a ). The transducers represented by transducers  162 A and  162 B are controlled by servo control signal  286 A and the transducers represented by transducers  162 C and  162 D are controlled by servo control signal  286 B. 
     A portion of beam  24  incident on optical cavity  230  at surface  228 A is reflected as beam  25  (see  FIG. 6   a ). As shown in  FIG. 5 , beam  25  is incident on non-polarizing beam splitter  108 , after reflection by mirrors  112 C and  112 D, and is transmitted as a measurement beam component of beam  109 . A second portion of beam  1022  is reflected by non-polarizing beam splitter  104  and a portion thereof is reflected by non-polarizing beam splitter  108 , after reflection by mirror  112 E and transmitted by phase retardation plate  72 , as a reference beam component of beam  109 . Beam  109  is a mixed beam with the planes of polarization of the measurement and reference beam components of beam  109  being parallel. 
     Beam  109  is detected by detector  150 , preferably by a quantum photon detector, to generate signal  152 . Signal  152  is transmitted to electronic controller, signal processor, and computer  600  and servo control signals  286 A and  286 B are generated. The description of the generation of servo control signals  286 A and  286 B is the same as the description of corresponding portions of the description given for generation servo control signals  186  of the third embodiment. For the fourth embodiment, information is obtained to control both the respective positions and orientations of mirrors  226 A and  226 B by known techniques such as modulating the position or orientation in one plane of one element at a frequency with a small amplitude and detecting an error in position by phase sensitive detection at the frequency. This procedure is repeated for all of the degrees of freedom of mirrors  226 A and  226 B sequentially or simultaneously using different frequencies for each of the different degrees of freedom. 
     The description of the generation of the reference cavity of reference object  130 R of the fourth embodiment is the same as corresponding portions of the description given for the reference cavity of reference object  130 R of the third embodiment. 
     The angle of incidence of beam  207 A at interface  243  is θ 4  as shown in  FIGS. 6   a  and  6   b . As a result of the non-normal angle of incidence, there is a phase shift introduced between near-field probe beams transmitted by adjacent wavelength or sub-wavelength apertures  30 . This phase shift φ 4  which is given by the formula
 
φ 4 =2η 4 k 1 b sin θ 4   (35)
 
where η 4  is the index of refraction of element  232 .
 
     The introduction of phase shift φ 4  may be used beneficially used in certain end-use applications such as in differential interferometric confocal near-field microscopy [see, e.g., previously mentioned U.S. Provisional Application entitled “Differential Interferometric Confocal Near-Field Microscopy” by Henry A. Hill]. 
     An advantage of the fourth embodiment is a reduced background because of the design of optical cavity  230 . 
     The remaining description of fourth embodiment is the same as corresponding portions of the description given for the third embodiment. 
     It will be evident to those skilled in the art that additional optical elements can be introduced into the optical path of beam  207  with an index of refraction such that the resonant conditions for optical cavity  230  are satisfied simultaneously for two different wavelengths without departing from the scope and spirit of the present invention. The resulting achromatic optical cavity can be used with source  1010  being configured to produced optical beam pulses at two different wavelengths. The reconfigured source  1010  can for example comprise two independent pulsed sources with the two beams being combined by a dichroic beam splitter. 
     Referring to the drawings,  FIG. 7  illustrates, in schematic form, the fifth embodiment of the present invention. The fifth embodiment generates enhanced transmission of an optical beam through an array of wavelength and/or sub-wavelength apertures with a pulsed source. The fifth embodiment further incorporates interferometric techniques to measure and monitor properties of optical cavities. Interferometric techniques offer advantages in increased signal-to-noise ratios, direct measurements of relative phases between optical beams, and the measurement of the properties of the optical cavities without the requirement of altering either the frequency of an optical beam and/or properties of the optical cavities. 
     The fifth embodiment comprises many elements performing like functions as elements of the fourth embodiment. Elements in  FIG. 7  with element numbers the same as element numbers of certain elements in  FIG. 5  are corresponding elements and perform similar functions as the corresponding elements of the third embodiment. 
     The optical cavity of the fifth embodiment generally indicated at element number  330  in  FIG. 5  is illustrated schematically in expanded form in  FIG. 8   a . Optical cavity  330  is a folded cavity comprising mirrors  326 A and  326 B, and Amici type lens  332 . Surfaces  327 A,  327 B,  333 B,  333 A, are antireflection coated for the wavelength of beam  1022 . Surfaces  328 A and  328 B have coatings with a high reflectivity. Interface  343  preferably has a high reflectivity. The description of aperture array element  342  is the same as the corresponding portion of the description given for aperture array element  142  of the first embodiment. 
     The resonant cavity of optical cavity  330  is defined by surfaces  328 A and  328 B and interface  343 . The general description of properties of optical cavity  330  is the same as corresponding portions of the description given for optical cavity  130  of the first embodiment. 
     As shown in  FIG. 7 , beam  1022  is incident on non-polarizing beam splitter  104  and a portion thereof is reflected by mirror  112 E as beam  24 . Beam  24  is transmitted by surface  327 A and incident on surface  328 A (see  FIG. 8   a ). The beam incident on surface  328 A excites optical cavity  330  with the build up of beam illustrated as elements  307 A and  307 B when resonant conditions corresponding to Eq. (3) of the first embodiment are satisfied. 
     The focal lengths of surfaces  328 A and  328 B are selected so that modes of optical cavity  330  are stable. The focal length of element  326 A is selected so that a stable transverse mode of optical cavity  330  is excited the beam incident on surface  328 A. The position and angular orientation of element  326 A is controlled by three transducers  162 A and  162 B (the third transducer is not shown in  FIG. 8   a ) and the position and angular orientation of element  226 B is controlled by three transducers  162 C and  162 D (the third transducer is not shown in  FIG. 8   a ). The transducers represented by transducers  162 A and  162 B are controlled by servo control signal  286 A and the transducers represented by transducers  162 C and  262 D are controlled by servo control signal  286 B. 
     A portion of beam  24  incident on optical cavity  330  at surface  328 A is reflected (see  FIG. 6   a ). As shown in  FIG. 5 , the reflected component of beam  24  is incident on non-polarizing beam splitter  108  and is reflected as a measurement beam component of beam  109  after reflection by mirror  112 F. A second portion of beam  1022  is transmitted by non-polarizing beam splitter  104  and a portion thereof first transmitted by phase retardation plate  72  and then transmitted by non-polarizing beam splitter  108  as a reference beam component of beam  109  after reflection by mirror  112 F. Beam  109  is a mixed beam with the planes of polarization of the measurement and reference beam components of beam  109  being parallel. 
     Beam  109  is detected by detector  150 , preferably by a quantum photon detector, to generate signal  152 . Signal  152  is transmitted to electronic controller, signal processor, and computer  600  and servo control signals  286 A and  286 B are generated. The description of the generation of servo control signals  286 A and  286 B is the same as the description of corresponding portions of the description given for generation servo control signals  186  of the third embodiment. For the fifth embodiment, information is obtained to control both the respective positions and orientations of elements  326 A and  326 B by known techniques such as modulating the position or orientation in one plane of one element at a frequency with a small amplitude and detecting an error in position by phase sensitive detection at the frequency. This procedure is repeated for all of the degrees of freedom of elements  326 A and  326 B sequentially or simultaneously using different frequencies for each of the different degrees of freedom. 
     The description of the generation of the reference cavity of reference object  130 R of the fourth embodiment is the same as corresponding portions of the description given for the reference cavity of reference object  130 R of the third embodiment. 
     The angle of incidence of beam  207 A at interface  243  is θ 5  as shown in  FIG. 8   a . As a result of the non-normal angle of incidence, there is a standing wave pattern produced introduced at interface  343 . Examples of the amplitudes of standing wave patterns is shown in see  FIG. 8   b . The anti-nodes of the standing wave patterns can be arranged to coincide with wavelength or sub-wavelength elements  30  and/or  32  by selection of the value of θ 5  and the optical path lengths of optical cavity  330  seen by beams  307 A and  307 B. The wavelength Λ 5  of the amplitude of the standing wave pattern is accordingly 
               Λ   5     =       p   ⁢           ⁢     λ   1           η   5     ⁢   sin   ⁢           ⁢     θ   5                 (   36   )             
 
where η 5  is the index of refraction of element  332  and p is a non-zero integer.
 
     The registration of anti-nodes with wavelength or sub-wavelength elements  30  and/or  32  by servo control signals  286 A and  286 B. The procedure described for the generation servo control signals  286 A and  286 B further comprises modulation of optical path lengths of optical cavity  330  seen by beams  307 A and  307 B and detecting changes in selected elements of measured signal values [S n ] by phase sensitive detection. The selected elements correspond to the those elements of elements  30  and/or  32  for which its desired to have registration with the anti-nodes. 
     An advantage of the fifth embodiment is a reduced background because of the design of optical cavity  330 . 
     Another advantage of the fifth embodiment is a potential for improved coupling efficiency of beam  1022  to near-field probe beams. 
     The remaining description of fifth embodiment is the same as corresponding portions of the description given for the fourth embodiment. 
     It will be evident to those skilled in the art that additional optical elements can be introduced into the optical path of beams  307 A and  307 B with an index of refraction such that the resonant conditions for optical cavity  330  are satisfied simultaneously for two different wavelengths without departing from the scope and spirit of the present invention. The resulting achromatic optical cavity can be used with source  1010  being configured to produced optical beam pulses at two different wavelengths. The reconfigured source  1010  can for example comprise two independent pulsed sources with the two beams being combined by a dichroic beam splitter. 
     Further embodiments of the invention include adapting the systems described above to operate in a transmission mode. Once such embodiment is shown in FIG.  10 . 
     Many elements of the embodiment shown in  FIG. 10  perform similar functions as elements of the earlier embodiment and are indicated in  FIG. 10  with the same element numbers as corresponding elements of the first embodiment shown in  FIG. 1   a.    
     Beam  20  is incident on non-polarizing beam splitter  102 , and a first portion thereof is transmitted as measurement beam  22 T. Measurement beam  22 T is next reflected by mirror  92  and then focused to a spot on substrate  112 T after reflection by mirror  90 . Substrate  112 T comprises a transparent substrate at the wavelength of beam  20  and an element  24 T including a resonant optical cavity and array of wavelength and/or sub-wavelength apertures. Element  24 T corresponds to optical cavity  130  of the first embodiment except that the element does not include scattering sites  32 . A portion of measurement beam  22 T focused to the spot is transmitted by the apertures of element  24 T as an array of near-field probe beams. The description of the apertures is the same as the corresponding portion of the description given for the array of apertures  30  of the first embodiment. The diameter of the spot is large enough span the array of apertures. 
     Sample  25  to be examined by the array of near-field beams is placed on the flat surface of Amici type lens  26 T. The array of near-field probe beams is transmitted by sample  25  as a transmitted beam  34  corresponding to beam  34  of the first embodiment with respect to subsequent processing by the apparatus of the fifth embodiment. 
     A second portion of beam  20  is reflected by mirror  102  as reference beam  50 T, as shown in FIG.  10 . Reference beam  50 T is transmitted through an aperture in lens  60  as reference beam  52  after reflection by mirrors  94 A,  94 B, and  94 C. Reference beam  52  then contacts reference object  20 R which includes an Amici lens and array of reflecting reference elements corresponding to transmissive reference elements  30 R in shown in  FIG. 2   d . The reflecting elements produce return reference beam  54  just as in the embodiment of  FIG. 1   a . The remaining description is the same as corresponding portions of the description given for the first embodiment. 
     Notably, in additional embodiments, the reflective reference elements described in reference to  FIG. 10  may replace transmissive reference elements of any of the earlier embodiments. Moreover, additional embodiments need not include resonant reference cavity. Furthermore, in yet even further embodiments, the reference object can be uniform reflective object, such as a flat or curved mirror, although such embodiments may couple less of the reference beam to interfere with the near-field signal beams than in the previsously described embodiments. 
     Other aspects, advantages, and modifications are within the scope of the following claims.