Abstract:
A combination of a focusing means, and a filtering means which naturally adjusts the cross-sectional area of a beam of electromagnetic radiation passed to the focusing means as a function of wavelength, optionally as an element of an ellipsometer or polarimeter system.

Description:
This Application Claims Benefit of 61/211,055 filed Mar. 26, 2009. 
    
    
     TECHNICAL FIELD 
     The present invention relates to a system of aperturing a focusing means by use of a filtering means to arrive at an optimum electromagnetic beam cross-sectional area passed by the filtering means, based on optimizing said cross-sectional area in view of conflicting effects of aberration and diffraction inherent in said focusing means, which, for each wavelength, vary oppositely to one another with electromagnetic beam cross-sectional area. More particularly the present invention is a combination of a focusing means, and a filtering means which naturally adjusts the cross-sectional area of a beam of electromagnetic radiation passed to the focusing means as a function of wavelength. 
     BACKGROUND 
     It is known that focusing means, such as refractive lenses and lens systems, cause both diffraction and aberration to occur in a beam of electromagnetic radiation with which is interacts. 
     It is also known that when the effective diameter of a beam of electromagnetic radiation which impinges on a focusing means is adjusted, the effects of diffraction and of aberration are affected oppositely. That is, as the beam cross-sectional area is increased, the effects of diffraction decrease, but the effects of aberration increase. This leads to a realization that, for each wavelength in the beam, there should be a beam cross-sectional area such that the focusing lens performs “optimally”. That is, there exists a cross-section area such that increase or decrease in cross-sectional area will cause combined diffraction or aberration to become worse, (ie. cause lens performance to be worse). 
     It is also well known that attenuation of the intensity of a beam of electomagnetic radiation which is caused to pass through a material is related to the extinction coefficient and thickness of the material via Beer&#39;s Law:
 
 Io=Ii ( e   −∝T ).
 
Therefore, either an increase in the value of extinction coefficient ∝, or a greater thickness (T) of a material, or a combination of both, can cause a greater attenuation of input intensity (Ii) of components of a beam of electromagnetic radiation which passes through a lens. This is to be contrasted with the situation where input Intensity (Ii) is attenuated by reflection or scattering from a surface of an aperture forming material. Further, it is noted that “reflection” implies a specular condition wherein an angle of incidence of an input beam of electromagnetic radiation component is equal to an angle of reflection; whereas “scattering”, while still indicating a deflection of a component of an electromagnetic beam away from transmission through a lens, does not have such a limitation on the angle at which a beam component is deflected.
 
     With the present invention in mind a computer search for Patents and Published Applications was conducted. A few references were identified which are interesting as they relate to aberration corrections. For instance, a patent to Lee et al., U.S. Pat. No. 6,994,808 describes a planar lens which is designed to compensate chromatic aberration. Another patent to Kimura, U.S. Pat. No. 6,865,025 provides another optical element for application in compensating aberration. And, a Published Patent Application by Miller et al., No. 2004/0032664 describes a color corrected lens. Other Patents and Published Applications identified are: 
     PUBLISHED APPLICATIONS 
     
         
         2009/0322928; 
         2009/0108190; 
         2006/0164734; 
         2005/0247866; 
       
    
     
       
         
               
             
               
               
               
             
           
               
                   
               
               
                 Patents: 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 7,495,762; 
                 7,281,921; 
                 7,248,420; 
               
               
                 7,274,472; 
                 7,190,525; 
                 5,336,885; 
               
               
                 7,251,410; 
                 7,070,405; 
                 4,832,464; 
               
               
                 6,824,813; 
                 7,027,156; 
                 4,650,279. 
               
               
                 6,449,028; 
                 6,916,584; 
                   
               
               
                 5,889,593; 
                 6,277,938; 
               
               
                   
               
             
          
         
       
     
     The above cited patents are not considered to be particularly relevant to a focusing means that optimisms its optical response regarding aberration v. diffraction on a per wavelength basis. 
     It is also well known that various materials and stacks of materials or the like have different Transmission v. wavelength characteristics. Patents known by the Inventor herein which are relevant are: U.S. Pat. Nos. 7,239,391; 7,295,313; 6,940,595; and 6,636,309. However, while said general knowledge that stacked materials present with specific response to different wavelengths exists, application of the effect as taught in the present Application is not found in the known prior art. This is particularly the case where application of aperturing and focusing of electromagnetic beams by a present invention system for naturally adjusting the effective cross-sectional area of a focusing means as a function of wavelength is applied in an ellipsometer, polarimeter or the like system. 
     Finally, patents disclosing other approaches, (eg. apodizing filters, spatial filters, graded lens etc.), to improving imaging performance in metrology systems by adjusting the index of lens material index are:
     No. 5,859,424 to Norton;   No. 6,738,138 to Wei;   No. 7,145,654 to Norton; and   No. 7,050,162.   

     Need exists for a system which provides wavelength specific material response mediated aperturing and focusing of electromagnetic beams, on a wavelength by wavelength basis, to the end that an optimum beam diameter, in view of both diffraction and aberration effects is approached over a range of wavelengths. 
     DISCLOSURE OF THE INVENTION 
     The present invention is a system for naturally adjusting the effective cross-sectional area of a focusing means as a function of wavelength, to improve the performance of the focusing means. Said system comprises, in either order:
         a) a focusing means for focusing an electromagnetic beam, selected from the group consisting of:
           a lens; and   a lens system comprising at least two elements; and   
           b) a filtering means for naturally adjusting the effective cross-sectional area of a transmitted beam of electromagnetic radiation, as a function of wavelength, said focusing means and said filtering means being functionally associated.       

     The design criteria of said filtering means is that the effective cross-sectional area of the electromagnetic beam passed by said filtering means to said focusing means is naturally adjusted with respect to wavelength, such that the performance of the focusing means is rendered approximately optimum in view of an inherent tradeoff between diffraction and aberration effects as a function of electromagnetic beam cross-sectional area. 
     The filtering means can absorb electromagnetic radiation of some wavelengths but not others, can reflect electromagnetic radiation of some wavelengths but not others, and/or scatter electromagnetic radiation of some wavelengths but not others. 
     The filtering means performs at least two selections from the group consisting of:
         it passes;   it reflects;   it scatters;
 
electromagnetic radiation of some wavelengths but not others.
       

     For each wavelength, the focusing means aberration effects increase with the effective cross-sectional area of a beam of electromagnetic radiation directed thereto, and for each wavelength, focusing means diffraction effects decrease with the effective cross-sectional area of a beam of electromagnetic radiation directed thereto. 
     The effective cross-sectional area of a beam of electromagnetic radiation directed thereto, is naturally adjusted by said filtering means to be approximately optimum based on determining a cross-over point between increasing aberration and decreasing diffraction effects as a function of said cross-sectional area, for at least one wavelength. 
     The cross-sectional area can be of a shape selected from the group consisting of:
         circular;   square;   rectangular;   oval; and   elliptical;
 
wherein progressively greater “effective radii” can be defined, referenced to a common origin. Different materials can be present between adjacently positioned radii.
       

     The focusing means and filtering means can comprise a modular lens and a modular filtering means, or can comprise an integrated lens and filtering means. 
     The focusing means and filtering means can comprise a modular lens system comprising at least two modular lens elements and at least one modular filtering means positioned at a location selected from the group:
         before a lens element;   after a lens element;   between said at least two lens elements.       

     The focusing means and filtering means can comprise a modular lens system comprising at least two modular lens elements and at least one filtering means integrated into at least one of said lens elements at a location selected from the group:
         before said lens element;   after said lens element.       

     The focusing means and filtering means can comprise a modular lens system comprising at least two modular lens elements, and at least one filtering means integrated into both lens elements, each thereof being at a location selected from the group:
         before said lens element;   after said lens element.       

     The filtering means can be of a constant thickness over its area, or not of a constant over its area, and/or can comprise at least two concentric regions of different materials, wherein a first material is present between a first effective radius and a second greater radius, and a second material is present between said second radius and a third even greater effective radius, all centered about a common origin. 
     As a relevant application of a present invention system as described above is in ellipsometer and polarimeter or the like systems, it is disclosed that such systems comprise:
         a source of electromagnetic radiation;   a polarization state generator;   a stage for supporting a sample;   a polarization state analyzer; and   a data detector.
 
Said ellipsometer, polarimeter or the like system further comprises, at least prior to said stage for supporting a sample
   a system for naturally adjusting the effective cross-sectional area of a focusing means as a function of wavelength, to improve the performance of the focusing means comprising, in either order:
           a) a focusing means for focusing an electromagnetic beam, selected from the group consisting of:
               a lens; and   a lens system comprising at least two elements; and   
               b) a filtering means for naturally adjusting the effective cross-sectional area of a transmitted beam of electromagnetic radiation, as a function of wavelength;
 
said focusing means and said filtering means being functionally associated.
   
               

     The design criteria of said filtering means is that the effective cross-sectional area of the electromagnetic beam passed by said filtering means to said focusing means is naturally adjusted with respect to wavelength, such that the performance of the focusing means is rendered approximately optimum in view of an inherent tradeoff between diffraction and aberration effects as a function of electromagnetic beam cross-sectional area. 
     The filtering means can absorb electromagnetic radiation of some wavelengths but not others. 
     The filtering means can reflect electromagnetic radiation of some wavelengths but not others. 
     The filtering means can scatter electromagnetic radiation of some wavelengths but not others. 
     The filtering means can perform at least two selections from the group consisting of:
         it passes;   it reflects;   it scatters;
 
electromagnetic radiation of some wavelengths but not others, wherein, for each wavelength, focusing means aberration effects increase with the effective cross-sectional area of a beam of electromagnetic radiation directed thereto and wherein for each wavelength, focusing means diffraction effects decrease with the effective cross-sectional area of a beam of electromagnetic radiation directed thereto.
       

     The effective cross-sectional area of a beam of electromagnetic radiation directed thereto, is then naturally adjusted by said filtering means to be approximately optimum based on determining a cross-over point between increasing aberration and decreasing diffraction effects as a function of said cross-sectional area, for at least one wavelength. 
     The focusing means and filtering means can comprise a modular lens and a modular filtering means. 
     The focusing means and filtering means can comprise an integrated lens and filtering means. 
     The focusing means and filtering means can comprise a modular lens system comprising at least two modular lens elements and at least one modular filtering means positioned at a location selected from the group:
         before a lens element;   after a lens element;   between said at least two lens elements.       

     The focusing means and filtering means can comprise a modular lens system comprising at least two modular lens elements and at least one filtering means integrated into at least one of said lens elements at a location selected from the group:
         before said lens element;   after said lens element.       

     The focusing means and filtering means can comprise a modular lens system comprising at least two modular lens elements, and at least one filtering means integrated into both lens elements, each thereof being at a location selected from the group:
         before said lens element;   after said lens element.       

     The filtering means can be of a constant thickness over its area, or not constant over its area and/or can comprise at least two concentric regions of different materials, wherein a first material is present between a first effective radius and a second greater radius, and a second material is present between said second radius and a third even greater effective radius, all centered about a common origin. 
     The present invention will be better understood by reference to the Detailed Description Section of this Specification, in combination with the Drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1   a   1  and  1   a   2  show an aperture which is made from various materials at various radial extents. 
         FIG. 1   b  shows that different wavelengths “see” a different aperture (AP) cross-sectional area. 
         FIG. 1   c  shows transmission characteristics for materials (A) and (ST) in  FIG. 1   a  which result in  FIG. 1   b  operational characteristics. 
         FIG. 2   a   1  shows a side view of a modular lens (L) with an aperture (AP) placed just therebefore. 
         FIG. 2   a   2  shows a side view of an integrated lens (L) and aperture (AP). 
         FIG. 2   a   3  a lens (L) can be a lens system comprising a plurality of elements. 
         FIG. 2   b   1  shows a front view of a circular lens (L) and aperture (AP). 
         FIGS. 2   b   2 - 2   b   5  show front views of various alternative lens shapes. 
         FIG. 2   c  shows the primary desired effect of the present invention. 
         FIG. 3  shows a plot of beam energy as a function of aperture (AP) Radius (r). 
         FIG. 4  demonstrates how aperture (PA) opening radius (r) affects resolution capability. 
         FIG. 5  demonstrates an ellipsometer and polarimeter (E) or the like system. 
     
    
    
     DETAILED DESCRIPTION 
     Turning now to the Drawings,  FIG. 1   a   1  shows an aperture (AP) which is made from various materials at various radial (r) extents. Radius (r 1 ) identifies a opening through which a electromagnetic radiation of a given wavelength can pass. Radius (r 2 ) shows a region of the aperture, outside the radius (r 1 ), which is made of material (A), and radius (r 3 ) shows a region beyond radius (r 2 ) which is a beam stopper (ST).  FIG. 1   a   2  also shows that the aperture (AP) can comprise additional areas made of various other materials, (eg. (MB) between r 1  and r 4 ). 
     Additional concentric rings of different materials can be present and the Drawings are to be considered demonstrative and not limiting. 
       FIG. 1   c  shows transmission characteristics for material (A) and beam stopper (ST) in  FIG. 1   a   1  which result in  FIG. 1   b  operational characteristics.  FIG. 1   b  shows that different wavelengths “see” a different aperture (AP) cross-sectional area, (eg. an opening radius varies between (r 1 ) and (r 2 ) with wavelength). This is because of the wavelength dependent response of material (A). It will be appreciated that Figures like  FIGS. 1   b  and  1   c , but for a  FIG. 1   a   2  embodiment also result, but with different Percent of Transmission (TR %) for the region between (r 4 ) and (r 2 ) based on the characteristics of material (ST). Any number of such Figures result based on the number of regions of different Materials, (eg. (MA), (Mb) and additional (Mc) etc.), and it is not believed necessary to show a multiplicity of embodiments in view of the examples provided by FIGS.  1 A 1 ,  1 A 2 ,  1   b  and  1   c.    
       FIG. 2   a   1  shows a side view of a Lens (L) with an aperture (AP) placed just therebefore.  FIG. 2   b   1  shows a front view of said lens (L) and aperture (AP). As indicated by  FIGS. 1   a   1 - 1   c , the aperture (AP) diameter (D) varies with wavelength.  FIGS. 2   b   2 - 2   b   5  show front views of various alternative lens shapes, namely square, rectangular, oval and elliptical.  FIG. 2   a   2  shows that the lens (L) and aperture (AP) can be merged into an integrated embodiment. Both the  FIG. 2   a   1  modular, and  FIG. 2   a   2  integrated embodiments are disclosed as the Present Invention in this Disclose.  FIG. 2   a   3  demonstrates that, for the purpose of this disclosure, a lens (L) can be, but need not be, a lens system comprising a plurality of elements, (eg. at least (LA) and (LB) elements).  FIG. 2   a   3  also demonstrates that an aperture (AP) (AP′) (AP″) can alternatively be placed either before (AP) or after (AP′) a Lens (LA), or between (AP″) two elements (LA) (LB), or simultaneously at any selected multiple of said locations. This is the case regardless of the number of Lenses and Filters present. Note,  FIG. 2   a   3  is not to be interpreted to imply that a lens system can not be comprised of more than two elements. 
       FIG. 2   c  shows the primary desired effect of the present invention. Such a plot will exist for each wavelength. Note that a lens performance criteria is optimized in view of offsetting aberration and diffraction effects. Changing the Diameter (D) to make it larger or smaller results in a lessened Lens Performance. 
       FIG. 3  shows a plot of beam energy as a function of aperture (AP) radius (r). A similar plot results for each wavelength. 
       FIG. 4  demonstrates how aperture (AP) opening radius (r) affects resolution capability. 
       FIG. 5  demonstrates that an ellipsometer and polarimeter or the like system (E) generally comprises a source (S) of electromagnetic radiation, a polarization state generator (PSG), a stage (STG) for supporting a sample (SAM), a polarization state analyzer (PSA) and a data detector (DET). The polarization state generator (PSG) and polarization state analyzer (PSA) can each comprise a polarizer or analyzer respectively, and either can further comprise a compensator. Note that focusing (FM) and collimating (CM) are also shown. The present invention  FIGS. 2   a   1   2   a   2  and  2   a   3  refractive lens (L) and aperture (A) (A′) (A″) can be applied at these locations. 
     It is noted that the terminology “naturally adjusted” as used in this Disclosure is to be interpreted to mean that a fliter material optically responds to different wavelengths differently, so that an effective aperture diameter, and therefore the cross-sectional area of a beam of electromagnetic radiation interacting with an associated focusing means, is different for differnet wavelengths. The purpose being to provide a beam cross-sectional area which is more “optimum” in view conflicting aberration and diffraction criteria. 
     Having hereby disclosed the subject matter of the present invention, it should be obvious that many modifications, substitutions, and variations of the present invention are possible in view of the teachings. It is therefore to be understood that the invention may be practiced other than as specifically described, and should be limited in its breadth and scope only by the Claims.