Patent Publication Number: US-2022214162-A1

Title: Triangulation-based optical profilometry system

Description:
TECHNICAL FIELD 
     The present application relates to triangulation-based optical profilometry systems. 
     BACKGROUND 
     Triangulation-based three-dimensional optical profilometry systems are employed as contact-less surface measurement/mapping systems. A projection system projects a luminous line onto a sample surface. An imaging system, disposed at an angle to the sample surface, images the projected line onto an image sensor. Based on standard principles of triangulation-based profilometry, distortions in the imaged line are used to calculate the surface profile along the portion of the sample surface over which the luminous line was projected. 
     Generally, a centerline of the imaged luminous line is used to determine the surface profile for the sample surface. Various methods can be used for computing the centerline of the imaged luminous line, one of the most popular being the computation of the centroid (also referred to as the first moment, center of mass, or center of gravity) of the brightness (irradiance) profile along the thickness of the imaged line. The centroid is then computed for each sampling position along the imaged line to generate the centerline. 
     In the interest of maximizing accuracy of the profilometry measurements, the projected luminous line is preferably thin, in order to capture a smaller cross-sectional area orthogonal to the lateral extent of the line (i.e. thickness of the line) Similarly, resolution of the imaging system is often optimized in order to better capture sample surface details across a lateral extent of the sample. 
     However, the fine resolution of triangulation-based profilometry systems that use pixel-based image sensors can lead to non-physical artifacts appearing in the centroid calculation, and therefore in the calculated surface profile. 
       FIG. 1  depicts an example image  40  of a luminous line projected onto a flat, tilted surface, as captured by a two-dimensional pixel array based image sensor. As the irradiance tracks diagonally across the image  40 , activation of different rows of pixels can been seen as one moves from left to right. A centroid line  46  extracted from the image of  FIG. 1  is illustrated in graph  45  of  FIG. 2 . A straight line  48 , representing the theoretical centroid profile associated to a luminous line that would hit a flat, tilted surface is also illustrated, for comparison. 
     As can be seen from the centroid line  46 , several jumps or “wiggles” in the calculated vertical positions of the centroid are present. These non-physical artifacts appear in the centroid calculation where the tilted irradiance line is only detected in one pixel row for several adjacent lateral points on the line, due to the thickness of the imaged line that is smaller than the vertical dimension of a pixel of the image sensor. Rather than diagonally crossing different pixels, some portions of the tilted image line remain within a single row of pixels. For instance, in three neighboring pixels, the imaged line could be incident on a top portion of the first pixel, a center portion of the second pixel, and a bottom portion of the third pixel. In the centroid calculation, however, the image could appear as a horizontal line as pixels do not generally report where on a given pixel the light is detected. 
     Some solutions have been proposed to address this issue. The discretization problem above can at least nominally be tackled by extending the imaged line over many pixels. One possible solution is thus simply to use an image sensor with higher resolution (smaller pixels), but the increased cost of high-resolution sensors can quickly become a limiting factor in such a solution. Depending on the particular system, it is also possible that no greater resolution image sensor is available or practical. 
     It has also been proposed to form a thicker luminous line on the sample surface under inspection. The corresponding image line formed on the image sensor will generally be thicker, and thus will cover a larger number of pixels along the vertical direction, aiding in diminishing this discretization problem. The thicker luminous line formed on the sample surface also results in decreased resolution along the direction orthogonal to the line, however the sampling area would increase as wider strips of the sample surface are gathered into the same line measurement. 
     In order to cover multiple pixels, defocusing the image of the projected line has also been proposed. In such a case, any point of the luminous line formed on the sample surface would be imaged over a plurality of pixels of the image sensor. This proposed solution would aid in maintaining a small sampling area by keeping a fine line projected on the sample surface. The lateral resolution would however be decreased, as each point along the line would be spread laterally across the image sensor as well, overlapping with adjacent lateral points along the line. 
     There therefore remains a desire for solutions related to addressing measurement artifacts in triangulation-based three-dimensional optical profilometry systems. 
     SUMMARY 
     It is an object of the present technology to ameliorate at least some of the inconveniences present in the prior art. Developers of the present technology have developed various embodiments thereof based on their appreciation of at least one technical problem associated with the prior art approaches to triangulation-based three-dimensional optical profilometry and, particularly, to measurement artifacts related to imaging resolution for surface measurement. 
     In order to aid in minimizing the non-physical artifacts (jumps or “wiggles”) in the calculated surface profile related to discretization issues in pixel-based image sensors, an optical profilometry system is presented herein with the following features in accordance with a first broad aspect of the present technology. An objective lens assembly is arranged to form an out-of-focus image of a sample plane on an image sensor. The system further includes a diaphragm with a non-circular aperture, disposed along an optical axis between the sample plane and the image sensor. The defocused image of a luminous line projected on the sample plane is then asymmetrically spread over the image sensor. The image of any given point along the luminous line is thus received at the image sensor as a defocused spot, elongated along a vertical direction to extend over a greater number of pixels of the image sensor in the vertical direction than in the lateral direction. The vertical centroid of the imaged line can then be calculated over multiple rows of pixels, diminishing the effect of the discrete pixel arrangement. As the defocus is less extensive along the lateral direction, aiding in maintaining the lateral resolution of the measurement. 
     In accordance with one broad aspect of the present technology, there is provided triangulation-based optical profilometry system for scanning a three-dimensional sample surface located at a sample plane of the system. The system includes a projection system for projecting a luminous line across the sample surface; an image sensor for converting images of the luminous line, as projected on the sample plane, into electrical signals; a processing unit communicatively connected to the image sensor for processing the electrical signals; an objective lens assembly for imaging the luminous line, as projected on the sample plane, onto the image sensor, the objective lens assembly defining an optical axis extending between the sample plane and the image sensor, a first direction orthogonal to the optical axis and being defined parallel to an extent of the luminous line as projected, a second direction being defined perpendicular to the first direction, the first and second directions defining a plane orthogonal to the optical axis; and a diaphragm disposed along the optical axis between the sample plane and the image sensor, the diaphragm defining a non-circular aperture therein, the aperture being defined by a first dimension and a second dimension perpendicular to the first dimension, the second dimension being greater than the first dimension, the diaphragm being rotationally oriented relative to the image sensor such that the first dimension is aligned with the first direction and the second dimension is aligned with the second direction, the objective lens assembly being arranged to form an out-of-focus image of the sample plane on the image sensor. 
     In some embodiments, the diaphragm, the objective lens assembly and the image sensor are arranged such that an image of a given point along the luminous line, as projected onto the sample surface and collected by the image sensor during operation of the system, exhibits greater defocus along the second direction than the first direction. 
     In some embodiments, the luminous line extends laterally across the sample plane; the first direction is a lateral direction; the second direction is a vertical direction; and the diaphragm, the objective lens assembly, and the image sensor are arranged such that an image of a given point along the luminous line, as projected onto the sample surface and collected by the image sensor during operation of the system, exhibits greater vertical defocus than lateral defocus. 
     In some embodiments, the image sensor is a two-dimensional array of pixels; and during operation of the system, the image of the given point of the luminous line extends over a greater number of pixels of the image sensor in the vertical direction than in the lateral direction. 
     In some embodiments, during operation of the system, the image of the given point of the luminous line on the image sensor extends vertically over at least two pixels of the image sensor. 
     In some embodiments, a normal defined by the sample plane is skewed by a first angle (γ) relative to the optical axis; and a normal defined by the image sensor is skewed by a second angle (γ′) relative to the optical axis. 
     In some embodiments, the first angle (γ) and the second angle (γ′) are arranged in a Scheimpflug configuration, such that the second angle (γ′) is chosen relative to the first angle (γ) according to the relation: 
     
       
         
           
             
               
                 γ 
                 ′ 
               
               = 
               
                 
                   tan 
                   
                     - 
                     1 
                   
                 
                 ⁡ 
                 
                   [ 
                   
                     
                       
                         S 
                         i 
                       
                       
                         S 
                         o 
                       
                     
                     ⁢ 
                     
                       tan 
                       ⁡ 
                       
                         ( 
                         γ 
                         ) 
                       
                     
                   
                   ] 
                 
               
             
             , 
           
         
       
     
     where S i  is an image distance measured from the objective lens assembly to the image sensor and S o  is an object distance measured from the sample plane to the objective lens assembly. 
     In some embodiments, the projection system includes at least one illumination source; and a projection optical assembly for projecting light from the illumination source onto the sample plane in the form of a line. 
     In some embodiments, the at least one illumination source is a laser source; and the luminous line is a laser line projected onto the sample plane. 
     In some embodiments, the image sensor is disposed at a defocus position shifted along the optical axis away from an image plane of the sample plane as imaged by the objective lens assembly. 
     In some embodiments, the objective lens assembly includes a plurality of lenses. 
     In some embodiments, the diaphragm is disposed at an aperture stop of the objective lens assembly. 
     In some embodiments, the diaphragm is disposed at an entrance pupil of the objective lens assembly. 
     In some embodiments, the diaphragm is disposed at an exit pupil of the objective lens assembly. 
     In some embodiments, the second dimension of the aperture is about four times greater than the first dimension. 
     In some embodiments, the aperture is generally rectangular in form. 
     In some embodiments, a shape of the aperture is one of a geometric stadium, an oval, a rhombus, and a rounded-corner rectangle. 
     In some embodiments, the image sensor is one of: a charge-coupled device (CCD), a complementary metal-oxide-semiconductor (CMOS) device, and a N-type metal-oxide-semiconductor (NMOS) device. 
     Quantities or values recited herein are meant to refer to the actual given value. The term “about” is used herein to refer to the approximation to such given value that would reasonably be inferred based on the ordinary skill in the art, including equivalents and approximations due to the experimental and/or measurement conditions for such given value. 
     For purposes of this application, terms related to spatial orientation such as vertical and lateral are as they would normally be understood with reference to an optical axis to which the vertical and lateral directions are orthogonal. Terms related to spatial orientation when describing or referring to components or sub-assemblies of the system, separately from the system, should be understood as they would be understood when these components or sub-assemblies are assembled in the system, unless specified otherwise in this application. 
     In the context of the present specification, unless expressly provided otherwise, a “computer” and a “processing unit” are any hardware and/or software appropriate to the relevant task at hand. Thus, some non-limiting examples of hardware and/or software include computers (servers, desktops, laptops, netbooks, etc.), smartphones, tablets, network equipment (routers, switches, gateways, etc.) and/or combination thereof. 
     Embodiments of the present technology each have at least one of the above-mentioned object and/or aspects, but do not necessarily have all of them. It should be understood that some aspects of the present technology that have resulted from attempting to attain the above-mentioned object may not satisfy this object and/or may satisfy other objects not specifically recited herein. 
     Additional and/or alternative features, aspects and advantages of implementations of the present technology will become apparent from the following description, the accompanying drawings and the appended claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a better understanding of the present technology, as well as other aspects and further features thereof, reference is made to the following description which is to be used in conjunction with the accompanying drawings, where: 
         FIG. 1  depicts an example image of a projected line as captured by a triangulation based three-dimensional optical profilometry system according to the prior art; 
         FIG. 2  illustrates a surface profile determined from the imaged line of  FIG. 1 ; 
         FIG. 3  schematically depicts a triangulation-based three-dimensional optical profilometry system according to the present technology; 
         FIG. 4  is a close-up view of some portions of the profilometry system of  FIG. 3 ; 
         FIG. 5A  is an example line as imaged by the profilometry system of  FIG. 3 ; 
         FIG. 5B  illustrates a surface profile determined from the imaged line of  FIG. 5A ; 
         FIG. 6  schematically depicts a side view of an objective lens assembly and diaphragm of the profilometry system of  FIG. 3 , the Figure further showing three particular positions of the diaphragm along an optical axis; 
         FIG. 7  illustrates the diaphragm of  FIG. 6 , as viewed along the optical axis of the objective lens assembly of  FIG. 6 ; 
         FIGS. 8 to 11  illustrate different alternative embodiments of the diaphragm of  FIG. 7 ; and 
         FIG. 12  schematically depicts the relative arrangement of some components of the profilometry system of  FIG. 3 . 
     
    
    
     The drawings are not necessarily to scale and may be illustrated by phantom lines, diagrammatic representations and fragmentary views. In certain instances, details that are not necessary for an understanding of the embodiments or that render other details difficult to perceive may have been omitted. It should further be noted that throughout the appended drawings, like features are identified by like reference numerals. 
     DETAILED DESCRIPTION 
     Reference will now be made in detail to various non-limiting embodiments for an optical system and components disposed therein. It should be understood that other non-limiting embodiments, modifications and equivalents will be evident to one of ordinary skill in the art in view of the non-limiting embodiments disclosed herein and that these variants should be considered to be within the scope of the appended claims. Furthermore, it will be recognized by one of ordinary skill in the art that certain structural and operational details of the non-limiting embodiments discussed hereafter may be modified or omitted altogether (i.e. non-essential). In other instances, well known methods, procedures, and components have not been described in detail. 
     A triangulation-based three-dimensional optical profilometry system  100  according to the present technology, also referred to herein as the system  100 , is schematically illustrated in  FIGS. 3 and 4 . The system  100  includes a projection system  110  for projecting light onto a sample, a sample plane  130  for receiving the sample, and an imaging assembly  140  for imaging part of the light reflected from the illuminated portion of the sample surface  54 . Each of the projection system  110 , the sample plane  130 , and the imaging assembly  140  will be described in more detail below. Depending on the specific embodiment or application, the system  100  could include additional components that need not be described herein, including but not limited to: support structures, mechanical stages, power supplies, control hardware and/or software, electronic systems, etc. 
     The general principle of operation of the triangulation-based three-dimensional optical profilometry system  100  is illustrated in  FIG. 3 . The projection system  110  produces a fan-shaped light beam  111  which generates a luminous line  113  spanning across the sample plane  130  along a lateral direction  106 , spanning a lateral extent of a sample  52  disposed on the sample plane  130 . As used herein, it should be noted that the “lateral” direction  106  simply indicates a direction orthogonal to a line connecting the projection system  110  and the imaging assembly  140  and generally parallel to the sample plane  130 . There is not meant to be suggested by the term lateral any specific orientation in space of either the system  100  or any sample measured therein. 
     The luminous line  113 , as projected across a sample surface  54  of the sample  52 , is then imaged by the imaging assembly  140 , which includes an objective lens assembly  142  and an image sensor  160 . As is illustrated, for samples  52  which have a smaller lateral extent than the luminous line  113 , portions of the sample plane  130  may also be imaged. It is also contemplated that the projection system  110  could be adjusted to project only onto the sample  52 . 
     As imaged by the imaging assembly  140 , the line  113  does not generally appear as a straight line. Instead, topological features of the sample  52  distort the luminous line  113 , as seen from the vantage point of the imaging assembly  140 . Topological features of the sample  52  which can distort the luminous line  113  include, but are not limited to: surface shape, curvature, surface steps, surface roughness, irregularities, and holes or gaps in the surface. For example, the close-up partial image of a portion of the sample surface  54  shows surface roughness which causes the luminous line  113  to appear to undulate. 
     The imaging assembly  140  then captures one or more images of the luminous line  113  formed on the sample  52  at a plurality of locations along a length of the sample  52  (the length being measured along a direction perpendicular to the lateral extent of the line  113 ). In accordance with the principles of optical trigonometric triangulation, the objective lens assembly  142  and the image sensor  160  are located and oriented such that local variations in height located on the portion of the sample surface  54  illuminated by the luminous line  113  are detected by corresponding vertical shifts in images of the luminous line  113 . A sample image  117  is illustrated as having been determined by a processing unit  170  (specifically a computer  170 ). 
     The image  117  is then processed by the computer  170  in order to correlate the line of the image  117  to the physical lateral extent and height of the sample surface  54 . For each individual position along the length of the sample  52 , a two-dimensional graph, illustrated by sample graph  119 , is then created. The horizontal x-axis of the graph  119  corresponds to the lateral position across the sample and the vertical z-axis is the determined height, based on the distortion of the projected straight luminous line  113  by the profile of the sample surface  54 . The deviations in the image  117  are correlated to an actual height variation of the sample surface  54 , as illustrated on the z-axis of the graph  119 , depending on parameters such as the angles of the projection system  110  and the imaging assembly  140  relative to the sample plane  130  and the magnification of the objective lens assembly  142 . As is mentioned above, a centroid of the imaged line along the vertical direction is calculated for each lateral position (along the x-axis) to determine the sample surface profile currently illuminated the projection system  110 . Finally, the process of imaging the luminous line  113  at a particular position along the length of the sample surface  54  is repeated as the luminous line  113  is swept along the length of the sample surface  54 . A three-dimensional map of the profile of the sample surface  54  can then be created by combining the graphs  119  collected across the length of the sample surface  54 . 
     In order to aid in minimizing the non-physical artifacts (jumps or “wiggles”) visible in the calculated surface profile illustrated in the example of  FIG. 2  and discussed above, the objective lens assembly  142  is arranged to form an out-of-focus image of the sample plane  130  on the image sensor  160 . The system  100  further includes a diaphragm  150  with a non-circular aperture  154  (see  FIG. 7 , described in more detail below). The diaphragm  150  is disposed along an optical axis  102  (defined by the objective lens assembly  142 ) between the sample plane  130  and the image sensor  160  such that the defocused image of the luminous line  113  is asymmetrically spread over the image sensor  160 . As is illustrated schematically in  FIG. 4 , the image of any given point along the luminous line  113  is received at the image sensor  160  as a defocused spot, elongated along a vertical direction  108  (perpendicular to the lateral direction  106  of the luminous line  113 ). 
     During operation of the system  100 , the image of each point of the luminous line  113  thus extends over a greater number of pixels of the image sensor  160  in the vertical direction  108  than in the lateral direction  106 . An example image of a luminous line projected on a tilted, flat surface is illustrated in  FIG. 5A , where it can be seen that the line is defocused along the vertical direction  108  and activates at least two pixels along the entire lateral extent of the line. This allows the vertical centroid of the imaged line  113  to be calculated over multiple rows of pixels, diminishing the effect of the discrete pixel arrangement as is illustrated in  FIG. 5B . As the defocus is less extensive along the lateral direction  106 , the lateral resolution is less affected than it would be in cases where a circularly uniform defocus is present. While in the present embodiment the image of each given point of the luminous line  113  extends over at least two pixels of the image sensor  160  in the vertical direction  108 , it is contemplated that the thickness of the imaged line  113  could extend over more pixels of the image sensor  160 . 
     While the particulars of any given embodiment could differ, components employed in the present embodiment of the system  100  will now be described in more detail, with continuing reference to  FIGS. 3 and 4 . 
     The projection system  110  includes an illumination source  112  and a projection optical assembly  114  for projecting light from the illumination source  112  onto the sample plane  130  in the form of a line. In the present embodiment, the illumination source  112  is a laser source  112  and the line projected onto the sample plane  130  is a laser line. It is contemplated that other light sources, including partially-coherent and incoherent light sources, could be used in some embodiments. In some embodiments, it is also contemplated that the illumination source  112  could include multiple light sources. For instance, in some embodiments the illumination source  112  could include a plurality of laser sources emitting at different wavelengths. The projection optical assembly  114  includes a plurality of lenses and a linear slit (not separately illustrated), although different assemblies of optical components are contemplated. 
     The projection system  110  projects the luminous line  113  onto the sample  52  disposed on the sample plane  130 . The sample plane  130  is the plane where the sample surface  54  should be located for proper operation of the system  100 . In some embodiments, the sample plane  130  could be defined by a sample stage or table for receiving the sample  52 . In some embodiments, the projection system  110  and/or the imaging assembly  140  could be positioned or adjusted such that the sample plane  130  generally aligns with the sample surface  54 . Depending on the particular light source and arrangement, it is contemplated that the luminous line  113  could be well defined at a plurality of different planes. In some cases, the luminous line  113  will get its minimum thickness at one particular distance from the projection system  110 , preferably at the distance of the sample plane  130 . 
     The luminous line  113  is then imaged from the sample  52  by the imaging assembly  140 . The imaging assembly  140  includes the image sensor  160 , an objective lens assembly  142  and a diaphragm  150  disposed therein. The objective lens assembly  142  and the diaphragm  150  will be described in more detail below. 
     The image sensor  160  converts images of the luminous line  113 , as projected on the sample plane  130  and imaged onto the image sensor  160  by the objective lens assembly  142 , into electrical signals. According to the present technology, the image sensor  160  is a two-dimensional array of pixels, specifically a charge-coupled device (CCD). Depending on the particular embodiment, it is contemplated that the image sensor  160  could be embodied by sensors including, but not limited to, complementary metal-oxide-semiconductor (CMOS) devices and a N-type metal-oxide-semiconductor (NMOS) device. 
     The system  100  includes a processing unit  170  communicatively connected to the image sensor  160  for processing the electrical signals generated by the image sensor  160 . The processing unit  170  is generally described as the computer  170  herein, but this is simply one example of a non-limiting embodiment. Depending on the particular embodiment of the system  100 , it is contemplated that the processing unit  170  could be implemented as various structures, including but not limited to: one or more processors in a computing apparatus, software supported by a computing apparatus, and processing boards (GPU, FPGA, etc.). As is mentioned above, the computer  170  receives the electrical signals representing the image of the projected luminous line  113  from the image sensor  160 . Based on those electrical signals, the computer  170  then calculates the centroid profile of the imaged line  113  to determine a physical profile of the sample surface  54 . 
     With further reference to  FIGS. 6 to 11 , the objective lens assembly  142  and the diaphragm  150  will now be described in more detail. As is mentioned briefly above, the optical axis  102  is defined by the optical axis of the objective lens assembly  142 . As is noted above, the lateral direction  106  is the direction orthogonal to a line connecting the projection system  110  and the imaging assembly  140  and generally parallel to the sample plane  130 . Generally, the lateral direction  106  is thus also parallel to the extent of the luminous line  113  as projected and orthogonal to the optical axis  102 . The vertical direction  108  is defined perpendicular to the lateral direction  106 . The vertical and lateral directions  106 ,  108  thus generally define a plane orthogonal to the optical axis  102 , as is illustrated in  FIG. 4 . 
     The objective lens assembly  142  includes a plurality of lenses  144  in the illustrated example of  FIG. 6 , specifically a pair of doublets  144 . It should be noted that this is simply one non-limiting embodiment according to the present technology. It is contemplated that the objective lens assembly  142  could include more lenses  144  than illustrated, or only a single lens  144  depending on particulars of the embodiment. 
     The diaphragm  150  is disposed along the optical axis  102  between the sample plane  130  and the image sensor  160 . In the illustrated embodiment, the diaphragm  150  has been inserted between the lenses  144  so that the diaphragm  150  is located at an aperture stop  146  of the objective lens assembly  142 . It is contemplated, however, that the diaphragm  150  could be disposed exterior to the objective lens assembly  142 , either on an object side or an image side of the objective lens assembly  142 . In some embodiments for example, the diaphragm  150  could be disposed at an entrance pupil  147  of the objective lens assembly  142 . In some other embodiments, the diaphragm  150  could be disposed at an exit pupil  149  of the objective lens assembly  142 . The particular choice of placement of the diaphragm  150  along the optical axis  102  could depend on a variety of factors including, but not limited to, physical constraints in the objective lens assembly  142  or the imaging assembly  140  and magnification of the objective lens assembly  142 . 
     It is further contemplated that in some embodiments, the objective lens assembly  142  could be an off-the-shelf lens assembly adapted for receiving a commercially-available diaphragm defining a circular aperture. The diaphragm  150  according to the present technology could then be inserted into the off-the-shelf lens assembly, in place of the round aperture diaphragm. 
     As is mentioned above, the diaphragm  150  defines therein a non-circular aperture  154 . In the present embodiment, the aperture  154  is in the shape of a rounded-corner rectangle, as shown in  FIG. 7 . Different aperture shapes could be implemented in the present technology, as will be described in further detail below. 
     With reference to  FIG. 7 , the aperture  154  is defined in size by two dimensions: a “vertical” dimension  156  and a “lateral” dimension  158  perpendicular to the vertical dimension  156 . The terms vertical and lateral dimension  156 ,  158  are used due to their alignment in the system  100  with the vertical and lateral directions  108 ,  106  when the diaphragm  150  is in use in the system  100 . It should be noted however that the diaphragm  150  could be differently oriented when considered separately from the system  100  without changing the relative sizing of the “vertical” and the “lateral” dimensions  156 ,  158 . 
     By the present technology, the vertical dimension  156  is greater than the lateral dimension  158 , such that a larger portion of the light incident on the diaphragm  150  is allowed to pass the aperture stop  146  in the vertical direction  108  than in the lateral direction  106 . In the present embodiment, the vertical dimension  156  is about four times greater than the lateral dimension  158 , but the ratio of the vertical dimension  156  to the lateral dimension  158  could be greater or smaller depending on the specific embodiment. 
     When assembled in the system, the diaphragm  150  is rotationally oriented such that the vertical dimension  156  is aligned with the vertical direction  108  and the lateral dimension  158  is aligned with the lateral direction  106 . As the objective lens assembly  142  is arranged to form an out-of-focus image of the sample plane  130  on the image sensor  160 , the non-circular aperture  154  produces a non-circular spot on the image sensor  160  for any given point on the luminous line  113 . Specifically, the spot on the image sensor  160  is generally oval and elongated along the vertical direction  108 , although the exact spot size and dimensions will vary with the specific embodiment of the diaphragm  150  and the objective lens assembly  142 . 
     As is noted above, this combination of the non-circular aperture  154  and the objective lens assembly  142  being arranged at a defocus position relative to the image sensor  160  allows the imaged line  113  to extend vertically over at least two rows of pixels to aid in diminishing the effect of pixel-based artifacts in centroid calculation of surface profiles. 
     In some embodiments, in place of the diaphragm  150  in the form of a rounded-corner rectangle, the system  100  could instead include differently shaped apertures. For instance, the system  100  could include a diaphragm  250  defining a rhombus-shaped aperture  254  (illustrated in  FIG. 8 ). In other embodiments, the system  100  could include a diaphragm  350  defining a geometric stadium-shaped aperture  354 , a diaphragm  450  defining a generally rectangular-shaped aperture  454 , or a diaphragm  550  defining an oval-shaped aperture  554  (illustrated in  FIGS. 9 to 11  respectively). In each of the apertures  254 ,  354 ,  454 ,  554 , the vertical dimension of the aperture is about 4 times the lateral dimension of the aperture. 
     As the image sensor  160  and the objective lens assembly  142  are arranged to create an out-of-focus image of the sample plane  130 , the sample plane  130  and the image sensor  160  are further arranged relative to one another in order to maintain a consistent defocus across the image plane on the image sensor  160 , in order to avoid varying spot size at different locations of the image sensor  160 . In the present embodiment, the sample plane  130  and the image sensor  160  are each skewed to the optical axis  102  of the system  100  according to a Scheimpflug configuration. In  FIG. 12 , the Scheimpflug configuration of the sample plane  130  and the image sensor  160  relative to the optical axis  102  is illustrated. 
     For simplicity of illustration, the objective lens assembly  142  is schematically depicted as a single thin lens. As will be generally understood in the art, distances such as image distance and object distance are calculated with respect to principal planes of the objective lens assembly  142 . 
     According to the Scheimpflug configuration, a normal  131  to the sample plane  130  is skewed by a first angle (γ) relative to the optical axis  102 , where a center of the sample plane  130  is disposed at an object distance S o  from the objective lens assembly  142 . A normal  161  to the plane of the image sensor  160  is then skewed by a second angle (γ′) relative to the optical axis  102 , where a center of the image sensor  160  is at an image distance S i  from the objective lens assembly  142 . 
     The angles (γ), (γ′) between the normals  131 ,  161  and the optical axis  102  are then arranged according to the relation: 
     
       
         
           
             
               γ 
               ′ 
             
             = 
             
               
                 
                   tan 
                   
                     - 
                     1 
                   
                 
                 ⁡ 
                 
                   [ 
                   
                     
                       
                         S 
                         i 
                       
                       
                         S 
                         o 
                       
                     
                     ⁢ 
                     
                       tan 
                       ⁡ 
                       
                         ( 
                         γ 
                         ) 
                       
                     
                   
                   ] 
                 
               
               . 
             
           
         
       
     
     While the angles (γ), (γ′) are chosen based on known distances S i , S o  in the example above, it is contemplated that the angles (γ), (γ′) could be constrained (for instance depending on mechanical restrictions on the system  100 ), and the distances S i , S o  could instead be adapted based on the constrained angles (γ), (γ′). It is also contemplated that different configurations other than the Scheimpflug configuration could be utilized to arrange the components of the system  100 . 
     It is noted that the foregoing has outlined some of the more pertinent non-limiting embodiments. It will be clear to those skilled in the art that modifications to the disclosed non-limiting embodiments can be effected without departing from the spirit and scope thereof. As such, the described non-limiting embodiments ought to be considered to be merely illustrative of some of the more prominent features and applications. Other beneficial results can be realized by applying the non-limiting implementations in a different manner or modifying them in ways known to those familiar with the art. 
     The mixing and/or matching of features, elements and/or functions between various non-limiting embodiments are expressly contemplated herein as one of ordinary skill in the art would appreciate from this disclosure that features, elements and/or functions of one embodiment may be incorporated into another implementation as appropriate, unless expressly described otherwise, above. Although the description is made for particular arrangements and methods, the intent and concept thereof may be suitable and applicable to other arrangements and applications.