Abstract: The object of the present invention is to provide a system and method to enable a person wishing to improve his vision capabilities to carry with him a training device and to be able to train his vision whenever and wherever he wishes. The current invention makes use of widely available and familiar infrastructure of hand held devices such as cellular phone and cellular network. Other mobile digital devices having visual display may be used, for example: Pocket PC, Palm computer electronic notebook, Personal Digital Assistant (PDA) and even some digital music players such as iPod. Training session comprises of displaying to the trainee sequence of images on the built in display of there hand held device and receiving his response to the displayed images.

Abstract: A deforming method for a deformable mirror having plural electrodes and a reflective membrane which are distorted by static voltages. The Zernike voltage template used to deform a deformable mirror is adapted for aberration correction by calibrating each component template according to the specificity of the mirror. The voltages applied to the electrodes to form a surface profile of the reflective membrane are measured based on the reflection light from the membrane. A certain number of voltage-by-electrode patterns each of which corresponds to a different reference profile of the reflective membrane and specifies each set of a voltage and an electrode to which the voltage is to be applied are stored preliminarily. The reflective membrane is deformed to a desired profile by superposing preliminarily stored voltage-by-electrode patterns. The deformation of the mirror is corrected by calibrating each template according to the operational environment.

Abstract: A slit lamp mounted eye imaging device for viewing wide field and/or magnified views of the retina or the anterior segment through an undilated or dilated pupil. The apparatus images posterior and anterior segments of the eye, and sections/focal planes in between and contains an illumination system that uses one or more LEDs, shifting optical elements, and/or aperture stops where the light can be delivered into the optical system on optical axis or off axis from center of optical system and return imaging path from the retina, thereby creating artifacts in different locations on retina. Image processing is employed to detect and eliminate artifacts from images. The device is well suited for retinal imaging through an undilated pupil, non-pharmacologically dilated, or a pupil as small as 2 mm. Two or more images with reflection artifacts can be created and subsequently recombined through image processing into a composite artifact-free image.

Abstract: Upon detecting a selection of an examination start button, a start and completion management unit starts an examination. The control unit switches an observation state to an infrared light observation by an observation switching unit. Next, an examiner performs alignment while observing an eye to be examined, and photographs the eye to be examined with a photographing unit. The start and completion management unit determines whether the examination is completed according to a selection of an examination complete button, and repeats the alignment until it is determined that the examination is completed.

Abstract: An opthalmological photographic apparatus includes an observation moving-image photographic unit configured to photograph an observation moving image of a subject's eye, a still-image photographic unit configured to photograph a still image of the subject's eye, an image display unit configured to display at least one of the observation moving image and the still image, and a display content control unit configured to cause the image display unit to display one of the observation moving image and the still image when the still-image photographic unit photographs a still image.

Abstract: The present invention relates to technology for, among other things, administering, and analyzing the results of, ophthalmic examinations. The technology involves generating a display on a display device to enable a first ophthalmic exam to be administered, receiving a request for results of a second ophthalmic exam, requesting the results of the second ophthalmic exam from a data source, receiving the results of the second ophthalmic exam from the data source, displaying the results of the second ophthalmic exam on the display device and enabling annotation or modification of the results displayed on the display device.

Abstract: A dynamic aperture, positioned in the path of light, includes a pair of parallel blades, a connecting member, a driving member, and a motor. The projection device includes a light source configured for generating light. The connecting member is fixed to the projection device and rotatably interconnects a same side of the blades. The driving member rotatably interconnects the opposite side of the blades so that the blades, the connecting member, and the driving member constituting a variable quadrangular frame. The motor is coupled to the driving member and is configured for rotating the driving member. Rotation of the driving member and restriction of the projection device to the connection member alter dimensions of the variable quadrangular frame and accordingly adjust a gap between the blades through which the generated light passes.

Abstract: A light source device includes a first light source, a second light source, a reflective assembly, and a condensing lens defining an optical axis. The first light source includes a first lamp and a first reflector reflecting light beams generated by the first lamp as first parallel light beams. The second light source includes a second lamp and a second reflector reflecting light beams generated by the second lamp. The first light source, the reflective assembly and the condensing lens are arranged in order along the optical axis. The second light source corresponds to the reflective assembly deviated from the optical axis. The reflective assembly reflects light beams reflected by the first reflector back to the first reflector, and reflects light beams from the second reflector to the condensing lens. The condensing lens condenses the first parallel light beams and the light beams reflected by the reflective assembly.

Abstract: A lens module includes a seat, a lens holder and a thermal dissipation structure. The seat includes a base plate and two sidewalls perpendicularly formed on a surface of the base plate. The lens holder is mounted on the seat between the two sidewalls. The thermal dissipation structure is mounted on the seat and thermally conducts with the lens holder for cooling the lens holder.

Abstract: A display apparatus that displays an image on a retina of a user, the display apparatus comprising: an image output unit (100) which includes a light source (101, 110), a wavefront shape change unit (102, 109), and a scan unit (103, 108) and is configured to output display light for displaying the image; and a deflection unit (104, 107) configured to deflect, toward an eye of the user, the display light outputted by the image output unit (100). The deflection unit (104, 107) has a deflection characteristic of suppressing image distortion caused by a change in relative position of the deflection unit (104, 107) with respect to a pupil of the user.

Abstract: A projection optical system receives light from a display device surface and enlarges and projects a display image thereon onto a screen surface. The projection optical system includes one or more reflective surfaces having an optical power between the display device surface and the screen surface, moves at least one optical device having an optical power to adjust focus and satisfies the following conditional formula: ?0.02<{(?1??2)?2}/{(?1+?2)?1}<0.

Abstract: A projection optical system which has a short total length but can project a high quality and large image. The projection optical system projects the displayed image on an image displaying surface onto a projection surface, and includes a lens system having a plurality of lenses, and one or more curved mirrors. Light flux of an enlarged image shooting out from the lens system to the projection surface is incident onto a mirror surface of the one of the curved mirrors first of all. A distance OAL and a distance Y satisfy a requirement (1) 20<OAL/Y<30, OAL being the distance between the image surface and the surface of the curved mirror nearest the projection surface and along an optical path shared by the most lenses of the lens system, and on the image surface, and the distance Y being the distance between the optical axis shared by the most lenses and an edge of the image surface which is farthest from the optical axis shared by the most lenses.

Abstract: First and second reflectors are provided. The first reflector has a function of reflecting a light ray emitted from a light source and directing it toward an image display element and the second reflector has a function of changing the direction of a light ray so as to be reflected by the first reflector which light ray is emitted from the light source and not reflected by the first reflector. An outer periphery shape of the second reflector is changed correspondingly to an effective area of a first array lens 10.

Abstract: An exposure apparatus which exposes a substrate via a liquid supplied between a projection optical system and the substrate, the apparatus comprises a gas supply-recovery mechanism configured to blow a gas around the liquid, wherein the gas supply-recovery mechanism includes a nozzle unit in which a supply port configured to supply the gas, and a recovery port which is arranged nearer to an optical axis of the projection optical system than the supply port and is configured to recover the gas are formed, and wherein the nozzle unit is configured such that a first portion which is adjacent to the supply port and is nearer to the optical axis than the supply port is closer to an image plane of the projection optical system than a second portion which is adjacent to the supply port and is farther from the optical axis than the supply port.

Abstract: An immersion liquid confinement apparatus confines an immersion liquid in an immersion area that includes a gap between a projection system and an object of exposure in an immersion lithography system. The apparatus also recovers the immersion liquid from the immersion area. The apparatus includes a confinement member and first and second liquid-permeable members. The confinement member includes an outlet and an aperture through which a patterned image is projected onto the object. The first liquid-permeable member covers the outlet and has a first surface that faces the object and a second surface opposite the first surface, the second surface contacting a first chamber. The second liquid-permeable member has first and second oppositely-facing surfaces, the first surface of the second liquid-permeable member contacts the first chamber, the second surface of the second liquid-permeable member contacts a second chamber that is different from the first chamber.

Abstract: An immersion lithographic apparatus is provided in which a maximum permissible velocity of the substrate relative to a fluid confinement structure that controls the immersion fluid is determined based on a property of the substrate to be exposed and, during the exposure process, the velocity of the substrate relative to the fluid confinement structure is limited to be below this maximum permissible velocity.

Abstract: A lithographic apparatus includes a fluid supply system configured to provide a cleaning fluid to a surface to be cleaned. The cleaning fluid includes from 25 to 98.99 wt % water; from 1 to 74.99 wt % solvent selected from one or more glycol ethers, esters, alcohols and ketones; and from 0.01 to 5 wt % surfactant.

Abstract: An exposure method that uses a substrate (M) held by a holding member (28) to perform exposure processing, comprising a holding process, which holds a prescribed region (AR3) of the substrate as the holding region by means of the holding member, and a deformation process, which selectively deforms one side of the holding region of the substrate held by the holding process with respect to the other side. According to the present invention, a prescribed region of the substrate is held as a holding region by means of a holding member, and one side of the holding region of said held substrate is selectively deformed with respect to the other side, so it is possible to selectively eliminate the nonlinear deformation components attributable to holding of the substrate with respect to one side from among the two sides of the substrate using the holding region as a reference.

Abstract: A lithographic apparatus includes an assembly of a plurality of flexible medium transfer lines and a line carrier, the liner carrier configured to moveably guide the plurality of flexible medium transfer lines from one connection point of the apparatus to another connection point, wherein at least one of the two connection points is movable. At least one of the flexible medium transfer lines includes an inner base layer having an outer low-friction layer provided thereon, the outer low-friction layer having lower friction capacities than the inner base layer so as to provide a smooth guiding of the at least one of the flexible medium transfer lines relative to the carrier and a neighbouring flexible medium transfer line during a movement of the at least one connection point.

Abstract: Imprint lithography may comprise generating a fluid map, generating a fluid drop pattern, and applying a fluid to a substrate according to the fluid drop pattern. The fluid drop pattern may be generated using a stochastic process such as a Monte Carlo or structured experiment over the expected range of process variability for drop locations and drop volumes. Thus, variability in drop placement, volume, or both may be compensated for, resulting in surface features being substantially filled with the fluid during imprint.

Abstract: An exposure apparatus may include: a stage configured to move a substrate; an optical unit configured to generate and project a plurality of laser beams; and a control unit configured to measure straightness of the stage by controlling the projection of the laser beams to an exposed surface of the substrate while moving the stage. A method to measure straightness of a stage in an exposure apparatus may include: placing a substrate on the stage; moving the stage and substrate; generating a plurality of laser beams; projecting the laser beams to the substrate on the stage; and measuring the straightness of the stage by projecting the laser beams to an exposed surface of the substrate.

Abstract: The disclosure provides projection objectives which may be used in a microlithographic projection exposure apparatus to expose a radiation-sensitive substrate arranged in the region of an image surface of the projection objective with at least one image of a pattern of a mask arranged in the region of an object surface of the projection objective. The disclosure also provides projection exposure apparatus which include such projection objectives, as well as related components and methods.

Abstract: Provided is an EUV light source which brings a target into the plasma state to radiate EUV light from the generated plasma. The target is one of a plurality of discrete targets. The surface area of each target is 1.5 times or more of that of a sphere which has the same material and the same mass as those of the target.

Abstract: An apparatus for fabricating a biochip is provided. The apparatus includes a reaction chamber which encapsulates the biochip to be sealed form an external environment. The apparatus further includes an exposure system which has a light source and a spatial light modulator. The spatial light modulator receives light from the light source and forms an optical image utilizing the light. The optical image is received by the biochip. The apparatus further includes a detection system which detects light proceeding form the biochip.

Abstract: An apparatus includes a stage configured to move a substrate, an optical system configured to project an image of a pattern on an original onto the substrate, an alignment detection system configured to detect an image of an alignment mark formed on the substrate and measure a position of the alignment mark, and a focus detection system having an index mark and configured to measure a height of the substrate by projecting an image of the index mark onto the substrate. The stage includes an alignment measurement mark and a focus measurement mark that has a positional relationship with the alignment measurement mark. The alignment detection system measures a position of the alignment measurement mark. The focus detection system measures a position of the image of the index mark by projecting the image of the index mark onto the focus measurement mark.

Abstract: A scanning exposure method is provided. A mask and a substrate are oppositely moved along a direction. The mask and the substrate are moved in at least two different uniform relative velocities during a one shot exposure, thus producing an exposed shot area of an expected size on the substrate.

Abstract: An apparatus and a method for detecting deformations of a vehicle component on a motor vehicle are disclosed, which are capable of unambiguously determining the location and temporal progression of the deformation, as well as the severity of the deformation, within a very short time after the deformation of the vehicle component begins. An emitter unit together with a detector unit is displaced relative to an aperture component disposed on the vehicle component upon deformation of the vehicle component. A beam path of a light beam between the emitter unit and the detector unit is interrupted or opened when the aperture component is displaced relative to the emitter unit, thereby changing an illumination intensity detected by the detector unit. A signal representative of the illumination intensity is transmitted from the detector unit to an evaluation unit.

Abstract: A distance measuring apparatus includes a light source unit generating reference light for distance measuring, a light receiving device receiving light reflected from an object to be measured, which has received the reference light, a mirror controlling a path of the reference light, and controlling a path of light, reflected from the object to be measured, toward the light receiving device, and a sensor lens focusing the light reflected from the mirror on the light receiving device. The sensor lens includes a lens portion refracting light, a flange portion provided around the circumference of the lens portion and including a coupling portion for fixing the sensor lens, and a light passing portion formed at the lens portion.

Abstract: Spectrometric apparatus that include an array of detector elements and exhibits a number of capabilities is disclosed. The elements can be responsive to incident radiation to produce an output signal that includes information from the incident radiation. A spectrally selective element can be located in an optical path between the radiation source and the array, with an analysis module responsive to the output signal operative to analyze spatial distribution of spectral information received by the array. The apparatus can also correct for differences in intensity and spectral variability for spectral image signals and/or compare the spectral image signals with a pattern in spatial-spectral coordinate space. Detector elements can be responsive to scattering, and spatial information in their output can be analyzed.

Abstract: A fiber optic optical subassembly configuration for monitoring fibers. The configuration includes a hollow container, a laser for emitting laser signals towards the fibers being monitored, a photodetector for monitoring reflected laser signals from the fibers being monitored and for monitoring laser output power, a beam splitter and an optical fiber. The optical fiber, disposed within the hollow container, has a coated end face surface, the laser emits signals toward and through the beam splitter, whereby a portion of the laser signal illuminates the photodetector, and another portion traverses down the optical fiber toward the coated end face surface and reflects off the coated end face surface toward the fibers that are being monitored, and reflects back from the fibers being monitored to the photodetector such that faults on the fibers can be detected.

Abstract: A measurement apparatus for measuring an optical fiber transmission line used to connect to an opposite apparatus, the measurement apparatus includes a transmission part for generating a measurement packet used for measuring a length of a first and second optical fiber transmission line, and transmitting the measurement packet to the opposite apparatus through the first optical fiber transmission line, a reception part for detecting the measurement packet returned from the opposite apparatus that perform a loopback processing of the measurement packet through the second optical fiber transmission line, a calculation part for calculating a packet transmission time which is a processing time required from the generation of the measurement packet to the detection of the measurement packet, and a measurement part for performing a measurement control of the length of the first and second optical fiber transmission line based on the packet transmission time calculated by the calculation part.

Abstract: Wavefront control techniques are provided for the alignment and performance optimization of optical devices. A Shack-Hartmann wavefront sensor can be used to measure the wavefront distortion and a control system generates feedback error signal to optics inside the device to correct the wavefront. The system can be calibrated with a low-average-power probe laser. An optical element is provided to couple the optical device to a diagnostic/control package in a way that optimizes both the output power of the optical device and the coupling of the probe light into the diagnostics.

Abstract: A sample (26) is illuminated by laser light and the resulting Raman spectrum (62) is dispersed at a high spectral resolution along one or more rows or columns of detector elements (60) of a CCD (34). The resulting charge is shifted in a direction Y? and binned in an output register 64 of the CCD. The dispersed spectrum is moved along the rows or columns in a direction X?, synchronously with the shifting of charge in the output register (arrow 72). Thus, data from a given wavenumber in the spectrum continues to accumulate in the output register during the movement. This enables data from a wide spectrum to be collected at high resolution, without the need to subsequently stitch blocks of data together in a computer, even where the CCD is arranged such that row-by-row transfer of charge towards the output register is orthogonal to the direction of dispersion.

Abstract: According to one embodiment of the present invention, a system for encoding an optical spectrum includes a dispersive element, a digital micromirror device (DMD) array, a detector, and a controller. The dispersive element receives light from a source and disperses the light to yield light components of different wavelengths. The digital micromirror device (DMD) array has micromirrors that modulate the light to encode an optical spectrum of the light. The detector detects the light that has been modulated. The controller generates an intensity versus time waveform representing the optical spectrum of the detected light.

Abstract: A filtrate monitoring device and a filtrate monitoring system, which can monitor a membrane-type water filtrating/purifying system at all times and which can flexibly adjust themselves to the contents and sizes of impurities, are provided. The filtrate monitoring device monitors the filtrate having passed through the membrane-type water filtrating/purifying device. The filtrate monitoring device comprises: imaging/detecting means for shooting images in the filtrate having passed through the filtrating/purifying device, on the filtrate flowing in an observation bath of a filtrate observing cell disposed midway of the branched filtrate pipeline, thereby to specify the particles contained in the filtrate, and/or optical detecting means disposed midway of the filtrate pipeline before or after branching.

Abstract: A rotation detection kit, comprising a source for generating at least a first polarized beam emitted along a propagation axis, a receiver comprising at least a first beam intensity sensor and an analyzer. The analyser comprises a first polarizer device for location in the at least first polarized beam between the source and at least first beam intensity sensor. The first polarizer device is configured such that the receiver can measure rotation between the source and the analyzer about a first axis that is non-parallel to the propagation axis based on the at least first beam intensity sensor's output.

Abstract: A film thickness measuring method can carry out measurement of a thickness of an oxide film more simply in a shorter time. The film thickness measuring method includes determining a thickness of an oxide film or thin film of a metal or alloy by solely using a phase difference ?, measured by ellipsometry, based on a predetermined relationship between the phase difference ? and the thickness of the oxide film or thin film of the metal or alloy.

Abstract: There is provided a method for determining residual errors, compromising the following steps: in a first step, a test plate comprising a first pattern is used, and in a second step, a test plate comprising a second pattern which is reflected and/or rotated with respect to the first step is used.

Abstract: A radiation detector is disclosed with a detector arrangement, which has a plurality of detector elements, by means of which a detector signal is obtained during operation of the radiation detector, and with a control device, wherein the detector elements each have a spectral sensitivity distribution, and are suited for generating signals. At least one detector element includes a compound semiconductor material, and this detector element is designed for detecting radiation in the visible spectral region. The radiation detector is designed such that the sensitivity distributions of the detector elements are used to form different spectral sensitivity channels of the radiation detector. A channel signal assigned to the respective sensitivity channel can be generated in these sensitivity channels using the detector elements, and the control device is designed such that the contributions of different channel signals to the detector signal of the radiation detector are differently controlled.

Abstract: In the fields of biosensing and the like, achievement of high sensitivity and high performance has been demanded in the concentration detection of target substances. In order to meet such demand, disclosed is an optical element utilizing the localized surface plasmon resonance, including: a dielectric substrate; a first group of metal microstructures in which a plurality of metal microstructures is supported on a dielectric substrate in an in-plane direction of the substrate; and a second group of metal microstructures in which a plurality of metal microstructures is disposed in the in-plane direction, and each of the metal microstructures is partially exposed to the outside; wherein the first group of metal microstructures and the second group of metal microstructures are laminated so as to be separated from each other by 100 nm or more.

Abstract: The present invention provides a long-range surface plasmon optical waveguide sensor which has a reduced loss of an electromagnetic wave, an increased sensitivity and limitation of detection and a high analysis speed, and enables fabrication of a sensor of various sizes such as a small-sized or lightweight system, etc.

Abstract: An information-acquiring device for acquiring information on an objective substance to be detected, which is provided with a sensing element that has a surface capable of fixing the objective substance to be detected thereon, and makes applied light change its wavelength characteristics in response to the fixed state of the objective substance to be detected onto the surface, a light source, and light-receiving means for receiving light emitted from the light source through the sensing element, has the light-receiving means and the light source arranged on the same substrate so that the light which has been emitted from the light source and has been transmitted through the sensing element can be led to the light-receiving means, and has means for varying the wavelength regions of each light incident on each of a plurality of the light-receiving means installed in an optical path from the light source to the light-receiving means.

Abstract: The invention relates to a spectrometer for material analysis and to a control method for a spectrometer. The spectrometer includes a radiant source (140) formed by multiple single radiation sources (141) having different central wavelengths, for generating a measuring signal, a measurement object (100) containing a material to be analyzed, at least one electrically tunable Fabry-Perot filter (120, 220) for the band pass filtering the measuring signal by at least two pass bands, and a detector (300, 400) for detecting said filtered measuring signals received from the measurement object (100).

Abstract: An optical coherence tomography device includes a wavelength scanning laser light source (10) provided with two Fabry-Perot resonators (13A, 13B) provided in a light path for laser oscillation. The values of FSR (free spectral range) of the Fabry-Perot resonators are set so as to be proximate to each other. The resonator length of at least one of the two Fabry-Perot resonators is periodically varied within a preset range to cause the two Fabry-Perot resonators (13A, 13B) to operate as a wavelength length varying filter of a narrow pass band capable of varying the selection wavelength by the vernier effect to output laser light that has wavelength temporally scanned.

Abstract: An object of the invention is to provide an optical reflectometry and an optical reflectometer, in which accurate measurement can be performed irrespective of a measurement distance. In the optical reflectometry and optical reflectometer according to the invention, in which a distribution of backscattered light intensity from a measurement target in an optical propagation direction is measured using Optical Frequency Domain Reflectometry (OFDR), a coherence monitor unit 12 that monitors a coherence property of a frequency sweep light source 1 is provided, and measurement result of a measuring unit 11 is corrected based on the monitor result of the coherence monitor unit 12.

Abstract: The invention relates to a system and to a corresponding method for optical coherence tomography having an interferometer (10) and a detector system (30, 31) which comprises a detector (30) for collecting the light reflected by a specimen (1) to be examined and has a sensitivity to the light reflected by the specimen (1). In order to reduce the times required for the most reliable possible recording of interference signals provision is made such that the sensitivity of the detector system (30, 31) to the light reflected by the specimen (1) and impinging on the detector (30) is modulated with a modulation frequency.

Abstract: A reference mark configuration for an interferometric miniature grating encoder readhead using fiber optic receiver channels is provided. The readhead may include “primary” fibers that provide reference mark primary signals processed to generate a reference signal with accuracy of approximately 0.2 microns. In some embodiments, a zone grating type reference mark may be embedded in a periodic scale grating, and configured such that it provides strong reference mark primary signals without disrupting periodic incremental measurement signals associated with the periodic scale grating. In one embodiment, the readhead may include “secondary” fibers used to generate reference mark secondary signals processed to generate a reference signal with accuracy of approximately 20 nanometers.

Abstract: A microscopy system and method allow observing a fluorescent substance accumulated in a tissue. The tissue can be observed at a same time both with visible light and with fluorescent light. It is possible to observe a series of previously recorded fluorescent light images in superposition with the visible light images. An end of the series of images may be automatically determined. A thermal protective filter may be inserted into a beam path of an illuminating system at such automatically determined end of the series. Further, the fluorescent light image may be analyzed for identifying a coherent fluorescent portion thereof. A representation of a periphery line of the coherent portion may be generated, and depths profile data may be obtained only from the coherent portion. An illuminating light beam for exciting the fluorescence may be modulated for improving a contrast of fluorescent images.

Abstract: The relative position of a test surface is sequentially changed from a reference position where a surface central axis is aligned with a measurement optical axis such that the measurement optical axis is sequentially moved to a plurality of annular regions obtained by dividing the test surface in a diametric direction. The test surface is rotated on a rotation axis whenever the relative position is changed. Measurement light that travels while being converged by a Mirau objective interference optical system is radiated to the rotating test surface, and a one-dimensional image sensor captures interference fringes at each of a plurality of rotational positions. The shape information of each annular region is calculated on the basis of the captured interference fringes at each rotational position, and the shape information is connected to calculate the shape information of the entire measurement region.

Abstract: This invention generally relates to accurately measuring image geometries in-line within a printing system. One or more two-dimensional array sensors may be located adjacent to a sheet of media printed with a predefined array of indicia marks so that the sensor field of view is contained within the plane of sheet transport. As the sheet is transported by the sensor, the sensors continuously record the locations of the indicia marks within its field of view. The spatial frequency of the indicia marks is arranged so that at least two indicia marks are within the field of view of the sensor at any instant for each of the process and cross-process directions. The two-dimensional array sensor can thus measure the absolute spacing between adjacent local indicia marks within the precision of the sensor construction. The cumulative spacing along each direction may then calculated to determine the overall dimensions of the indicia marks array.