Patent Publication Number: US-2016235291-A1

Title: Systems  and  Methods  for  Mapping  and  Evaluating  Visual  Distortions

Description:
TECHNICAL FIELD 
     The present disclosure relates to systems and methods for mapping and evaluating visual distortions, and in particular to systems and methods for mapping and evaluating visual distortions caused by metamorphopsia. 
     BACKGROUND 
     Visual perception is a complex process in which light passes through the cornea, lens, and various humours of the eye before being received by the retina where it is detected by photoreceptors. Nervous signals generated by these photoreceptors are processed by the brain, and more particularly by the visual cortex. A substantial portion of what we perceive as vision is provided by the cognitive processing of the visual cortex. This cognitive processing is not fully developed at birth and must be “learned” during the developmental stages of the visual system (i.e. in the early years of sight). Such cognitive processing includes, for example, mapping stimuli received at particular points of the retina into points of a coherent image. For instance, after cognitive processing, the images of both eyes are perceived as being in registration, inverted images on the retina are perceived as being non-inverted, straight lines are perceived as straight rather than curved (despite the retina itself being curved), and so on. 
     Metamorphopsia is a condition in which a portion of the retina is displaced relative to its original placement (i.e. its placement during the developmental stages of the visual system). The associated cognitive processing does not generally fully adapt to this displacement, resulting in distortions in the visual perception of images received by the retina. For example, images perceived by a subject with metamorphopsia may be skewed, of a different size, in a different location, or otherwise different than the same images perceived by a subject with a normal retina. 
     Metamorphopsia has a variety of causes, the most common of which is age-related macular degeneration (AMD). Although there is not currently a cure for AMD, there are a variety of treatments which can slow (or even temporarily reverse) its progression. Such treatments include photodynamic therapy, ocular injections of anti-vascular endothelial growth factor, and nutritional supplements such as lutein, meso-zeaxanthin and zeaxanthin. Accordingly, there is a general desire to detect metamorphopsia in subjects at an early stage. Further, there is a general desire to evaluate the severity of particular cases of metamorphopsia in order to assess the efficacy of a particular treatment. 
     The quality of life of a subject may be severely and adversely impacted by metamorphopsia (e.g. by a progressively worsening inability to perform daily tasks such as driving, reading, recognizing faces, etc.). Accordingly, it is particularly advantageous in many circumstances to determine the severity of the visual distortions perceived by the subject. The severity of visual distortions may often not be directly determinable from the severity of the physiological displacement of the affected portion of the retina (e.g. as measured via optical coherence tomography), due to the complexities of the cognitive processes discussed above. 
     Detection of metamorphopsia and the subsequent measurement of the efficacy of treatments are commonly performed by presenting subjects with an Amsler grid, such as the example Amsler grid  100  shown in  FIG. 1 . Subjects fixate one eye on fixation target  102  and provide anecdotal feedback on, among other things, the size and location of distortions in grid lines  104 . This approach can present challenges in ensuring that results are comparable between assessments, since even small variations in the subject&#39;s viewing distance, the subject&#39;s fixation point, and/or other viewing conditions may significantly impact the perceived size and location of distortions. Further, measurement by conventional Amsler grid may be relatively imprecise. 
     There have been several recent attempts to collect more precise measurements of visual distortions for the purpose of quantifying, mapping, and (ultimately) correcting the distortions. Some such developments are disclosed, for example, in U.S. Pat. Nos. 5,589,897, 5,892,570, and 8,708,495. Such attempts generally involve providing a pattern which is adjustable by the subject. The subject may then adjust the pattern until it appears “correct” (e.g. until the grid lines of Amsler grid  100  appear straight). 
     Due to the complexity of the visual system, existing methods may still be prone to inaccuracies, inefficiencies, and/or imprecision in certain circumstances. Accordingly, there is a general desire for systems and methods for mapping and evaluating visual distortions caused by metamorphopsia which ameliorate at least some of the deficiencies discussed above and/or other deficiencies. 
     The foregoing examples of the related art and limitations related thereto are intended to be illustrative and not exclusive. Other limitations of the related art will become apparent to those of skill in the art upon a reading of the specification and a study of the drawings. 
     SUMMARY 
     The following embodiments and aspects thereof are described and illustrated in conjunction with systems, tools and methods which are meant to be exemplary and illustrative, not limiting in scope. In various embodiments, one or more of the above-described problems have been reduced or eliminated, while other embodiments are directed to other improvements. 
     An aspect of the present disclosure provides a method for mapping visual distortions perceived by a subject. The method may be performed by a processor in communication with a display. The method includes displaying, at the display, a fixation target to the subject. The method includes receiving, at the processor, an indication corresponding to an identification of a distortion region by the subject. The distortion region has a location determined relative to the fixation target. The method includes displaying, at the display, an adjustable reference pattern to the subject. The adjustable reference pattern is at least partially within the distortion region and the adjustable reference pattern is adjustable within the distortion region and fixed outside the distortion region. The method includes receiving, at the processor, an indication corresponding to an adjustment by the subject of the adjustable reference pattern within the distortion region. The adjustment is at least partially complementary to visual distortion perceived by the subject in the distortion region. The method includes determining, at the processor, a fixed reference pattern based on the adjustment of the adjustable reference pattern. 
     The method further includes displaying, at the display, one or more adjustable patterns to the subject. Each of the one or more adjustable patterns is at least partially within the distortion region, and each of the one or more adjustable patterns is adjustable within the distortion region and fixed outside the distortion region. The method further includes receiving, at the processor, one or more indications corresponding to one or more adjustments by the subject of the one or more adjustable patterns within the distortion region. The one or more adjustments are at least partially complementary to visual distortion perceived by the subject in the distortion region. The method further includes determining, at the processor, a distortion map based on the one or more adjustments of the one or more adjustable patterns. 
     An aspect of the present disclosure provides systems for performing the methods described above. Systems according to particular embodiments may comprise a processor configured to perform one or more of the methods described herein. Non-transitory computer-readable media may be provided with instructions, which (when executed by a suitably configured processor), cause the processor to perform one or more of the methods described herein. 
     According to another aspect of the invention, the methods described herein are encoded on computer readable media and which contain instructions executable by a processor to cause the processor to perform one or more of the methods described herein. 
     According to another aspect of the invention, systems are provided wherein processors are configured to perform one or more of the methods described herein. 
     Further aspects of the invention and features of example embodiments are illustrated in the accompanying drawings and/or described in the following description. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings illustrate non-limiting example embodiments of the invention. 
         FIG. 1  is an example of a prior art Amsler grid. 
         FIG. 2A  is a schematic cross-sectional illustration of an eye. 
         FIG. 2B  is a graph of visual acuity (on the vertical axis) against retinal eccentricity (on the horizontal axis). 
         FIG. 2C  is a photograph of a portion of the macular region of an example retina. 
         FIG. 2D  is a photograph of a portion of the peripheral region of an example retina. 
         FIG. 3A  is an illustration of an example image received on an example normal retina. 
         FIG. 3B  is an illustration of an example perception of the image of  FIG. 3A  by an example subject with a normal retina. 
         FIG. 4A  is an illustration of an example image received on an example retina with metamorphopsia. 
         FIG. 4B  is an illustration of an example perception of the image of  FIG. 4A  by an example subject with a retina with metamorphopsia. 
         FIG. 5A  is an illustration of an example perception of an example image which has been corrected to account for the subject&#39;s reported visual distortions, wherein the perception comprises double vision. 
         FIG. 5B  is an illustration of an example perception of an example image which has been corrected to account for the subject&#39;s reported visual distortions, wherein the perception comprises an uncorrected portion. 
         FIG. 5C  is an illustration of an example perception of an example image which has been corrected to account for the subject&#39;s reported visual distortions, wherein the perception is skewed. 
         FIG. 6A  is an illustration of an example corrected image received on the example retina of  FIG. 4A . 
         FIG. 6B  is an illustration of an example perception of the image of  FIG. 6A  by the example subject of  FIG. 4B . 
         FIG. 7  is a block diagram illustrating an example method for mapping visual distortions. 
         FIG. 8A  is a schematic side elevation view of an example system for mapping visual distortions. 
         FIG. 8B  is a schematic plan view of the system of  FIG. 8A . 
         FIG. 9A  is an example calibration display prior to a subject&#39;s placement of boundary lines. 
         FIG. 9B  is the example perception of a calibration display of  FIG. 9A  during the subject&#39;s placement of an example first boundary line. 
         FIG. 9C  is the example calibration display of  FIG. 9A  after the subject&#39;s placement of example first and second boundary lines. 
         FIG. 9D  is the example perception of a calibration display of  FIG. 9A  during the subject&#39;s placement of an example third boundary line. 
         FIG. 9E  is the example calibration display of  FIG. 9A  after the subject&#39;s placement of example third and fourth boundary lines. 
         FIG. 9F  is the example perception of a calibration display of  FIG. 9A  during the subject&#39;s placement of an example fifth boundary line. 
         FIG. 9G  is the example calibration display of  FIG. 9A  after the subject&#39;s placement of example fifth and sixth boundary lines. 
         FIG. 9H  is the example perception of a calibration display of  FIG. 9A  during the subject&#39;s placement of an example seventh boundary line. 
         FIG. 9I  is the example calibration display of  FIG. 9A  after the subject&#39;s placement of example seventh and eighth boundary lines. 
         FIG. 9J  is the example calibration display of  FIG. 9A  after placement of eight example boundary lines and depicting an example region defined therebetween. 
         FIG. 9K  is the example calibration display of  FIG. 9A  after placement of eight example boundary lines and depicting another example region defined therebetween. 
         FIG. 9L  is the example calibration display of  FIG. 9A  after a subject&#39;s identification of a distortion region according to an alternative embodiment. 
         FIG. 10A  is a grid illustrating various example resolution regions according to an example embodiment. 
         FIG. 10B  depicts various example adjustment rows according to the resolution regions of  FIG. 10A . 
         FIG. 11A  is an example adjustment display prior to a subject&#39;s adjustment of an example adjustment row. 
         FIG. 11B  is the example adjustment display of  FIG. 11A  after adjustment of the example adjustment row of  FIG. 11A . 
         FIG. 11C  is the example adjustment display of  FIG. 11A  prior to a subject&#39;s adjustment of an example adjustment column. 
         FIG. 11D  is the example adjustment display of  FIG. 11A  after adjustment of the example adjustment column of  FIG. 11C . 
         FIG. 11E  is an example display of an example visual reference based on the adjustment row of  FIG. 11B  and adjustment column of  FIG. 11C . 
         FIG. 11F  is an illustration of an example perception of the display of  FIG. 11E  by an example subject with a retina with metamorphopsia. 
         FIG. 12A  is an example adjustment display comprising the example visual reference of  FIG. 11E  prior to a subject&#39;s adjustment of a further example adjustment row. 
         FIG. 12B  is an example adjustment display comprising the example visual reference of  FIG. 11E  after the subject&#39;s adjustment of the further example adjustment row of  FIG. 12A . 
         FIG. 13A  is an example verification pattern according to an example embodiment. 
         FIG. 13B  is the example verification pattern of  FIG. 13A  rotated by approximately 45°. 
         FIG. 14A  is an example selection display showing a user selection of a distorted region. 
         FIG. 14B  is an example refinement display showing a constrained region for further adjustment based on the user selection of  FIG. 14A . 
         FIG. 14C  is an example perception of the example refinement display of  FIG. 14B . 
         FIG. 15A  is an example perception map or distortion map illustrated with distorted gridlines in an example distortion region. 
         FIG. 15B  is an expanded view of a portion of the example map of  FIG. 15A  illustrating an example method for determining a severity of displacement based on an area displaced. 
         FIG. 15C  is an expanded view of a portion of the example map of  FIG. 15A  illustrating an example method for determining a severity of displacement based on the displacement of a point from its original (pre-distortion) position. 
         FIG. 15D  is an expanded view of a portion of the example map of  FIG. 15A  illustrating an example method for determining a severity of displacement based on the local change in displacement of a point. 
     
    
    
     DETAILED DESCRIPTION 
     Throughout the following description, specific details are set forth in order to provide a more thorough understanding of the invention. However, the invention may be practiced without these particulars. In other instances, well known elements have not been shown or described in detail to avoid unnecessarily obscuring the invention. Accordingly, the specification and drawings are to be regarded in an illustrative, rather than a restrictive sense. 
     Methods described herein are implemented by suitably configured computers and/or suitably configured processors. Throughout the disclosure where a processor, computer or computer readable medium is referenced such a reference may include one or more processors, computers or computer readable media in communication with each other through one or more networks or communication mediums. The one or more processors and/or computers may comprise any suitable processing device, such as, for example, application specific circuits, programmable logic controllers, field programmable gate arrays, microcontrollers, microprocessors, computers, virtual machines and/or electronic circuits. The one or more computer readable media may comprise any suitable memory devices, such as, for example, random access memory, flash memory, read only memory, hard disc drives, optical drives and optical drive media, or flash drives. Further, where a communication to a device or a direction of a device is referenced it may be communicated over any suitable electronic communication medium and in any suitable format, such as, for example, wired or wireless mediums, compressed or uncompressed formats, encrypted or unencrypted formats. 
     One or more processors and/or computers in communication with each other through one or more networks or communication mediums may be collectively or individually referred to herein as a “computer system”. Actions performed by a computer system may be understood to be performed by one or more processors, and/or may be understood to be performed by other components of one or more computers in the computer system (e.g. at an input device such as a keyboard, touch screen, computer mouse, etc.; at an output device such as a display, an audio speaker, a haptic feedback motor, etc.; and/or at other components). 
     Aspects of the present disclosure provide systems and methods for mapping and evaluating visual distortions caused by metamorphopsia. The methods involve showing a subject initial patterns which may be adjusted to appear non-distorted to the subject. A reference pattern within the subject&#39;s region of distorted vision is generated from the initial patterns and is used to promote suitable head position and eye fixation throughout the subsequent steps of the methods. Further patterns within the distorted region are shown to the subject and are adjusted to appear non-distorted to the subject. Patterns may be non-adjustable outside of the distorted region. The adjusted patterns may be used to define a distortion map which allows images to be distorted in a complementary way so that the images appear non-distorted to the subject. The distortion map may undergo interpolation to add detail to the information provided by the adjusted patterns. 
     Systems according to particular embodiments may comprise a processor configured to perform such methods using a display. Non-transitory computer-readable media may be provided with instructions, which (when executed by a suitably configured processor), cause the processor to perform such methods. 
     In order to fully appreciate certain aspects of the present disclosure, particular features of the typical human eye should be brought to mind  FIG. 2A  is a schematic cross-sectional illustration of an example eye  200 . The depicted portion of eye  200  is substantially covered by an example retina  202  (and thus substantially opposes the portion of the eye housing the iris, lens, cornea, etc.). Retina  202  comprises several regions, including the macula  204 , the fovea  206 , and the foveola  208 . Retina  202  is partially obstructed by the optic disc  212 , which overlays the optic nerve (not shown). 
     Retina  202  is an arrangement of photoreceptors, which are divided into cones (smaller, densely-packed photoreceptors which provide higher resolution vision as well as colour sensitivity) and rods (larger photoreceptors which provide low light vision and other functions). These photoreceptors are not distributed uniformly or in regular geometric array. In general, cones tend to be more concentrated towards the center of retina  202  (particularly within macula  204 ), and rods are primarily found further from the center of retina  202 . For instance,  FIG. 2C  is a photograph of a macular region  260  (i.e. located within macula  204  of example retina  202 ) which primarily comprises cones  262 .  FIG. 2D  is a photograph of a peripheral region  270  (i.e. located outside of macula  204 ) which comprises a much greater proportion of rods  272 . 
     Due to the greater proportion of cones  262  in macula  204 , visual acuity tends to be much greater within macula  204  than outside macula  204 . Macula  204  typically has a diameter of approximately 6 mm (i e an angular diameter of approximately 18°). Cones  262  are even more densely packed within fovea  206 , which typically has a diameter of approximately 1.5 mm (i e an angular diameter of approximately 5°). Foveola  208  typically comprises only cone photoreceptors, and provides the greatest visual acuity of any region of retina  202  in a typical eye. Foveola  208  typically has a diameter of approximately 0.35 mm (i.e. an angular diameter of approximately 1.2°) Nerve endings are also more densely concentrated in fovea  206  and foveola  208 , resulting in much more visual information being transmitted from these areas. 
     The relative visual acuity of each region of example retina  202  is depicted in chart  230  of  FIG. 2B . Axis  242  represents visual acuity, and ranges from 0 (corresponding to no vision) to 1 (corresponding to peak visual acuity, found in the center of foveola  208 ). Axis  244  represents the angular position of each point in the retina relative to the center of foveola  208 . Line  232  depicts the visual acuity of various portions of the retina. For example, point  238  corresponds to the visual acuity of foveola  208  at its center. The portion of line  232  within range  236  corresponds to the visual acuity of fovea  206 . The portion of line  232  within range  234  corresponds to the visual acuity of macula  204 . Region  240  corresponds to the blind spot coinciding with optical disk  212 . 
     As shown in  FIG. 2B , visual acuity drops off sharply outside of foveola  208 . Threshold  246  corresponds to maximal visual acuity (e.g. 20/20 vision), which is only achieved in the depicted example at point  238 . Threshold  248  corresponds to 50% of the visual acuity at threshold  246 , (e.g. 20/40 vision), and is only achieved in the depicted example within approximately 0.75 mm (i e within an angular distance of approximately 2.5°) of the center of foveola  208 . 
       FIG. 3A  shows an example image  300 A received on an example normal retina. The image comprises, in this example, a straight line  302 . Gridlines  304  represent the arrangement of a normal retina without displacement (i.e. without metamorphopsia). Axes  306  and  308  are provided for reference, and correspond to nominal positions on the retina. Line  302  lies substantially straight on the retina (curvature of line  302  due to the shape of curvature of the eye is omitted for the sake of example), which is reflected by the registration of line  302  with gridlines  304 .  FIG. 3B  shows a corresponding perception  300 B of image  300 A by a subject with a normal retina. Perceived line  312  corresponds to line  302 . Perceived line  312  is perceived as straight, as indicated by the registration of line  312  with gridlines  314 . Axes  316  and  318  substantially correspond to axes  306  and  308 , respectively, although axes  316  and  318  correspond to positions in perceived space (rather than positions on the retina). As would be expected,  FIGS. 3A and 3B  illustrate an accurate perception of a straight line by a normal eye. 
     It will be appreciated that, in the above and following examples, straight lines (such as line  302 ) are used for the simplicity of illustration. Other patterns, including geometric shapes (e.g. squares, rectangles, circles, ellipses, parallelograms, triangles, etc.), irregular shapes (e.g. inkblots, outlines of arbitrary shapes, etc.), photographs, and/or any other suitable visual indicia may be used. 
       FIG. 4A  shows an example image  400 A received on an example retina with metamorphopsia. Gridlines  404  are distorted to reflect the displacement of portions of the retina. The same straight line  302  is projected onto the metamorphopsia-affected retina in the same location as in  FIG. 3A , although (due to the displacement of a portion of the retina) it is sensed by different photoreceptors.  FIG. 4B  shows a corresponding perception  400 B of image  400 A by a subject with the example metamorphopsia-affected retina of  FIG. 4A . Due to the displacement of a portion of the retina, perceived line  412  is perceived as being non-straight within the perceived space indicated by gridlines  414 . This distortion is due to the physiological displacement of a portion of the retina as well as subsequent cognitive processing which interprets the stimuli received by the retina and transmitted to the brain. 
     The present disclosure provide systems and methods for mapping the distortions perceived by a subject, thereby generating a distortion map which maps points in an image (such as image  400 A) to points in a perceived space (such as in perception  400 B). A distortion map, once generated, may be used to “correct” images shown to the subject so that the images are perceived by the subject without distortion. This may be done by distorting images in a manner complementary to the distortions represented by the distortion map. Such corrective distortions (e.g. as represented by a perception map complementary to the distortion map) may be used for diagnostic purposes, to produce corrective optical and/or electronic devices, and/or for other purposes. 
     A variety of issues can arise when generating a distortion map and/or when correcting images. In particular,  FIGS. 5A, 5B, and 5C  show examples of some potential issues. 
     For example, if the subject&#39;s eye is permitted to move during testing, the position of the image on the retina may shift. Such movement is relatively common, since involuntary ocular tremors, ocular drift, and microsaccades may cause the eye to move during the course of testing. In such circumstances, the distortion map may reflect a translational distortion in one eye which is not truly present (or is present to a lesser or greater extent). The same translational distortion may not be determined during testing of the other eye, which may lead to double vision, as shown in perception  500 A of  FIG. 5A . Rather than perceiving a single straight line  502  corresponding to line  302 , the subject may experience double vision, e.g. by perceiving a displaced line  504  in one eye which is out of registration with line  502  in the other eye. Accordingly, in addition to addressing localized distortions (e.g. in addition to straightening a distorted line), it is desirable to ensure that the subject&#39;s eye remains fixed on a particular point in the image (e.g. image  400 A) during generation of the distortion map so that the corrected image will be properly aligned in both eyes. 
       FIG. 5B  depicts an alternative example perception  500 B resulting from a subject&#39;s example eye movement. In this case, rather than introducing a translational error, the distortion map may incorrectly reflect a perceived distortion in a portion of the image (e.g. image  400 A). For example, a subject may be presented with image  400 A (which, as depicted, is perceived as distorted in the range from −2 to 2 along axis  306 ), and the subject may over-or under-report distortion in a particular location (e.g. in the vicinity of row 0 on axis  306 ) due to microsaccades, a shift in the subject&#39;s fixation point, and/or due to other eye movement resulting in image  400 A falling on a different area of the subject&#39;s retina. Such eye-movement-induced error may result in an under- or over-correction of the corrected image, resulting in distorted perceptions such as perception  500 B. 
       FIG. 5C  depicts an example perception  500 C resulting from a subject adjusting portions of a distortion map corresponding to portions of a retina which are not displaced (i.e. portions where there is no true distortion). For example, a subject may adjust distorted portions of an image along the periphery of the image and subsequently adjust remaining portions of the image so as to ensure that the lines remain straight. It is generally more difficult to determine whether lines are parallel, horizontal, vertical or otherwise spatially oriented than it is to determine whether they are straight. This can give rise to a straight perceived line  508  which is out of registration with the perceived space indicated by gridlines  414 . 
       FIG. 6A  depicts an example image  600 A comprising a corrected line  604 . Gridlines  404  correspond to the same metamorphopsia-affected retina as shown in  FIG. 4A . In this example, corrected line  604  is perceived as straight line  612 , as shown in perception  600 B of  FIG. 6B . Notably, in this example, corrected line  604  is not merely the geometric inverse of perceived line  412  of  FIG. 4B . This helps to demonstrate that the relationship between how a subject may perceive a particular “normal” pattern and its corresponding corrected pattern may be more complex, in some circumstances, than merely finding the inverse of the distorted perception of the pattern. Accordingly, it may be advantageous in some circumstances to generate a perception map from the distortion map, and to generate approximations of images as perceived by the subject based on the perception map. 
       FIG. 7  depicts an example method  700  for generating a perception map. Method  700  may be considered to comprise several sub-methods, namely a calibration method  710 , a reference pattern generation method  730 , a distortion mapping method  750 , and a perception map generation method  770 . 
     Calibration method  710  comprises block  712  which involves calibrating a system for mapping distortions to present images so that they are received at the subject&#39;s retina in a consistent way between mappings. Such a system may, for example, comprise system  800 , as shown in  FIGS. 8A and 8B . For the purpose of the following disclosure, reference will generally be made to system  800  and its components with the understanding that the methods described herein may be performed by other suitably-configured systems. System  800  comprises an ophthalmic forehead and chin rest, and particularly comprises a support  804  for receiving the head of a subject  802  (subject  802  is not a component of system  800 , but is shown for the purpose of better illustrating the functionality of support  804 ). Support  804  may comprise a chin rest  808  and/or a head rest  806 . The head and chin of subject  802  may be secured to chin rest  808  and/or head rest  806  in order to limit head movement (particularly movement towards and/or away from a display  810 ). 
     Display  810  is provided facing support  804 . Display  810  may be in communication with a computer system  811  (for the purposes of this disclosure, “in communication with” includes being integrated with display  810 ), which may control display  810  to display graphical indicia such as pattern  814  to subject  802 . In some embodiments, display  810  has sufficient resolution to display graphical indicia without significant pixelation, aliasing, and/or other visual artifacts. Display  810  is preferably sufficiently large and positioned sufficiently near to support  804  to accommodate a field of view  820  which includes the subject&#39;s distorted areas of vision. In some embodiments, display  810  accommodates a field of view of at least 25° (i.e. having angles  818  and/or  828  of at least 25°) along at least one axis (e.g. along horizontal axis  308 ). In some embodiments, the center of display  810  is directly in front of the eye  803  of user  802 ; that is, the surface of display  810  may be perpendicular to the line of sight of user  802 . 
     Further, display  810  is preferably calibrated to provide an accurate image; that is, display  810  is preferably calibrated to display images centered in the screen and geometrically true (i.e. without stretching, compressing, or cropping the image). Display  810  may display images with uniform linear scaling. In some embodiments, display  810  displays images which are adjusted so as to be geometrically true when received at the retina, even though such adjustment may result in the images being deformed at the surface of display  810 . For example, a flat display  810  positioned close to a subject may result in an image which is displayed geometrically truly at the surface of display  810  to not be geometrically true at the subject&#39;s retina, since the center of display  810  may be closer to the subject&#39;s retina than the edges of the display. System  800  may be provided with the distance from the subject&#39;s eye to display  800  (e.g. as measured relative to the center of display  810 ) as well as the size of the display and/or the physical or angular size of the image to be displayed. On the basis of this or other information, system  800  may cause adjusted images  810  to be displayed to the subject which account for angular distortions caused by varying distances between the surface of display  810  and the subject&#39;s retina. In some embodiments, if display  810  is known to introduce one or more inaccuracies to displayed images, system  800  may be calibrated to take into account (e.g. counteract) such inaccuracies. 
     System  800  may be configured to present images to subject  802  with consistent angular sizes. However, displays  810  generally display images based on a linear size (e.g. expressed in pixels, inches, or the like). Therefore, in order to provide consistently-sized images to the retina of subject  802 , the physical dimensions of at least a part of system  800  must be known. In some embodiments, distance m indicated by line  812  between eye  803  (or support  804 ) and display  810  may be predetermined, measured, and/or otherwise determined. For example, distance m may be measured manually and input into computer system  811 , and/or computer system  811  may control the position of display  810  and/or support  814  to enforce a particular distance m. In some embodiments, where a range of acceptable distances m are available, display  810  is positioned at the maximum acceptable distance from support  804  (e.g. the largest distance available which provides at least a 25° field of view at display  810 ). 
     Once the distance m has been determined, the linear size L of an image displayed on display  810  may be determined according to the following equation: 
     
       
         
           
             L 
             = 
             
               2 
                
               m 
                
               
                   
               
                
               tan 
                
               
                 A 
                 2 
               
             
           
         
       
     
     where A is the angular size of the image to be displayed on display  810 . Although angular measurements are generally presented herein in degrees, they may alternatively or additionally be presented in radians. For example, the above equation is expressed in radians. 
     Correspondingly, the angular size A of an image having a known linear size L (such as a test image displayed during calibration) may be determined according to the following equation: 
     
       
         
           
             A 
             = 
             
               2 
                
               
                 tan 
                 
                   - 
                   1 
                 
               
                
               
                 L 
                 
                   2 
                    
                   m 
                 
               
             
           
         
       
     
     where A, L and m have the meaning discussed above. 
     In some embodiments, system  811  may display images based on retinal image sizes—that is, the size of an image as received on the retina of subject  802 . Based on the angular size A, system  811  may determine the retinal size R of an image according to the following equation: 
     
       
         
           
             R 
             = 
             
               L 
                
               
                 d 
                 m 
               
             
           
         
       
     
     where L and m have the meaning discussed above and d is the distance from the lens to the retina of eye  803  of subject  802 . The retinal image size R provides a common basis of measure that may be used across different implementations and different subjects. Retinal image sizes may, in some circumstances, be used in conjunction with distances of retinal disturbances as measured using optical coherence tomography and/or other techniques. 
     The dimensions l of display  810  and/or a portion of display  810  may be used to drive display  810  to display the image at the appropriate linear size (e.g. if L is intended to be 10 centimeters wide and the width of display  810  is 20 centimeters, then display  810  may be driven to display the image across 50% of the width of display  810 ). The dimensions l may be predetermined, measured, and/or otherwise determined. For example, a pattern  814  may be displayed on display  810  and measured. For instance, pattern  814  may comprise a straight line stretching diagonally across display  810  (assuming a rectangular display  810 ) between two predetermined display coordinates. In some embodiments, pattern  814  may be selected to be as large as possible so as to reduce the proportionate magnitude of error in measurement. For instance, pattern  814  may comprise a line stretching from one corner of display  810  to a diagonally-opposing corner. Alternatively, or in addition, dimensions of display  810  and/or a portion thereof, such as vertical dimension  816  (l v ) horizontal dimension  826  (l h ), and/or a diagonal dimension (not shown) may be predetermined or otherwise determined. 
     Computer system  811  may determine the maximum linear size required to display images in the subsequent tests. If that linear size exceeds the dimensions of display  810 , then computer system  810  may reduce the viewing distance m between display  810  and subject  802 , display a scaled-down version of one, some, or all images during the test, select a different display  810  of a suitable (larger) size, and/or take other action. Alternatively, or in addition, computer system  811  may present provide direction to an operator to perform one or more of those options. Alternatively, or in addition, computer system  811  may prompt an operator to choose between two or more such options. 
     At various times this disclosure will refer to subject  802  and/or an operator of system  800  interacting with system  800 . It will be understood that subject  802  and/or an operator of system  800  may interact with computer system  811  via input device  813  and/or via any other suitable device (e.g. a computer terminal in communication with system  800 , a mobile device, a computer mouse, a joystick, a rotary knob, and/or any other input device known in the art or later discovered). In some embodiments, subject  802  may also be an operator of system  800 . 
     Returning to  FIG. 7 , once the system (e.g. system  800 , as described above) has been calibrated, method  700  may proceed to block  714  which involves determining a distortion region. By determining the region of the field of view  820  of subject  802  which is distorted, method  700  and/or system  800  may prevent subject  802  from adjusting portions of test patterns which lie outside of the distortion region (and thereby avoid introducing certain errors to the distortion map).  FIGS. 9A, 9B, 9C, 9D, 9E, 9F, 9G, 9H, 9I, 9J, 9K and 9L  illustrate example methods of identifying a distortion region. 
       FIG. 9A  shows an example calibration display  902 A (which may be displayed to subject  802  by display  810 ). Display  902 A comprises a fixation target  906  for subject  802  to fixate eye  803  on. Fixation target  906  may comprise a dot, a crosshair (sometimes referred to by the inventor(s) as an “X”), and/or any other suitable shape. Fixation target  906  may have a visual angular size (e.g. an angular diameter) of approximately 0.5°. Fixation targets  906  which are no larger than approximately 0.5° have been found to promote fixation stability in some circumstances. 
     In example display  902 A, no boundary lines are shown. In some embodiments, display  902 A is not shown to subject  802  (e.g. block  714  may begin with display  902 B, discussed below). In some embodiments, display  902 A comprises a test pattern (such as an Amsler grid, a multi-resolution grid as shown in  FIG. 10A , and/or some other pattern) to assist subject  802  in identifying general areas in field of view  820  where distortions are present. Subsequently, display  902 B may be displayed to subject  802 . 
       FIG. 9B  shows an example perception of calibration display  902 B. Display  902 B comprises a boundary line  910 . In the depicted example, the perception of boundary line  910  is distorted near to fixation target  906 . Boundary line  910  is actually straight, so it can be determined that boundary line  910  passes through a distortion region which happens to be near fixation target  906 . Subject  802  may move boundary line  910  until it lies just outside of the distortion region (i.e. until it appears straight). Subject  802  may be constrained in the movement of boundary lines such as boundary line  910  so that boundary lines may only be moved orthogonally to the direction of the line. For example, since boundary line  910  runs horizontally, subject  802  may only be permitted to move boundary line  910  vertically. Subsequently, display  902 C may be displayed to subject  802 . 
       FIG. 9C  shows an example calibration display  902 C. Boundary lines  912  and  914  have been set by subject  802  to lie just outside of the distortion region; boundary lines  912  and  914  lie on opposing sides of that region. For example, boundary line  912  may correspond to boundary line  910  after boundary line  910  has been moved vertically upwards to lie outside of the distortion region. After confirming the location of boundary line  912 , subject  802  may similarly set the location of a parallel boundary line  914 . Subsequently, display  902 D may be displayed to subject  802 . 
       FIG. 9D  shows an example perception of a calibration display  902 D. Dashed lines  908  correspond to previously-set boundary lines (in this case, boundary lines  912 ,  914 ). Dashed lines  908  may be displayed to subject  802  (and may or may not be dashed) or may be hidden from view. A new boundary line  920  is provided. As with boundary line  910 , subject  802  may move boundary line  920  until it lies just outside of the distortion region. Boundary line  920  may run in any direction. In some embodiments, and in the depicted example, boundary line  920  runs in a direction orthogonal to previously-set boundary lines  912 ,  914 . Subsequently, display  902 E may be displayed to subject  802 . 
       FIG. 9E  shows an example calibration display  902 E. As with boundary lines  910  and  914 , boundary lines  922  and  924  have been set by subject  802  to lie just outside of the distortion region and on opposing sides thereof. Subsequently, display  902 F may optionally be displayed to subject  802 . Alternatively, the distortion region may be defined based on the area enclosed by lines  908 ,  922 ,  924  (see  FIG. 9K  for an example of this, discussed below). 
       FIG. 9F  shows an example perception of a calibration display  902 F. A new boundary line  930  is provided. As with boundary lines  910  and  920 , subject  802  may move boundary line  930  until it lies just outside of the distortion region. Boundary line  930  may run in any direction. In some embodiments, and in the depicted example, boundary line  930  runs in a direction diagonal to one or more of the previously-set lines  908 . Subsequently, display  902 G may be displayed to subject  802 , as shown in  FIG. 9G . Boundary lines  932  and  934  have been set by subject  802  substantially as described above. Subsequently, display  902 H may be displayed to subject  802 . 
       FIG. 9H  shows an example perception of a calibration display  902 H. A new boundary line  940  is provided. Subject  802  may move boundary line  940  substantially as described above. In some embodiments, and in the depicted example, boundary line  940  runs in a direction diagonal to one or more of the previously-set lines  908  and orthogonal to boundary line  930 . Subsequently, display  902 I may be displayed to subject  802 , as shown in  FIG. 9I . Boundary lines  942  and  944  have been set by subject  802  substantially as described above. Subsequently, display  902 J may be displayed to subject  802 . 
       FIG. 9J  shows an example calibration display  902 J. Distortion region  950  is defined between lines  908 . In the depicted example, distortion region  950  is determined to be the intersection of the areas between previously-defined pairs of parallel boundary lines  912  and  914 ,  922  and  924 ,  932  and  934 , and  942  and  944 . 
       FIG. 9K  shows an example calibration display  902 K. An alternative example distortion region  960  is defined between lines  908  (which correspond to the boundary lines  908 ,  922 , and  924  of  FIG. 9E ). In the depicted example, distortion region  960  is determined to be an ellipse defined between lines  908 . In an alternative embodiment, a distortion region may be determined to be the intersection of the areas between previously-defined pairs of parallel boundary lines  912  and  914  as well as  922  and  924  (which, in this example, would result in a rectangular distortion region), substantially as described above with reference to  FIG. 9J . 
       FIG. 9L  shows an example calibration display  902 L. An alternative example distortion region  970  is shown. In the depicted example, it is not necessary for boundary lines  908  to have been defined. Distortion region  970  may be defined by a subject  802  selecting a location, size, and/or shape for distortion region  970  (e.g. via input device  813 ). 
     It is not necessary that distortion regions  950 ,  960 ,  970  exactly correspond to the distortion perceived by subject  802 . Indeed, in most circumstances, distortion regions  950 ,  960 ,  970  will be slightly larger than the distortion perceived by subject  802 . However, it is generally advantageous for distortion region  950 ,  960 ,  970  to fully enclose the distortion perceived by subject  802 , and to include relatively little of the surrounding non-distorted area. 
     If subject  802  perceives multiple distortion regions, the above-described process of block  714  may be repeated until all distortion regions of interest have been identified. For the sake of simplicity, the union of all such identified distortion regions will be referred to simply as “the distortion region” in the following disclosure. 
     Returning to  FIG. 7 , method  700  (and, more particularly, calibration method  710 ) may continue to block  716  which involves selecting a representation for patterns to be displayed to subject  802 . As is discussed in greater detail below, patterns may be presented to subject  802  during method  700  at various times (including, in some embodiments, during the process of block  716 ). In some embodiments, these patterns comprise arrays of indicia (such as circles, squares, other geometric shapes, irregular shapes, images, and/or other indicia) which may be connected by a line. One such pattern is shown in  FIG. 10B , which provides variously-sized indicia  1014 ,  1024 , and  1034  (in this example, represented as dots) connected by variously-sized lines  1016 ,  1026 , and  1036 . Although in some circumstances providing lines is advantageous, in some embodiments indicia are provided without lines, or with other connecting features. In some embodiments, indicia have an angular size in the range of 0.1° to 0.5°, with larger sizes within that range generally being selected for patients with less visual acuity. In some embodiments, connecting lines have a thickness in the range of 0.05° and 0.1°. In some embodiments, connecting lines have a thickness in the range of 5% to 15% the angular size of their corresponding indicia. In some embodiments, connecting lines have a thickness that is not based on the angular size of their corresponding indicia. 
     The extent and severity of metamorphopsia may vary from subject to subject, as can relative visual acuity. Indicia of different sizes, shapes, and colors may appear to a particular subject to be more or less distorted than other indicia. Different size ratios between indicia and their corresponding lines may also, or alternatively, impact a subject&#39;s perception of distortion. Accordingly, subject  802  may be presented with several patterns, simultaneously and/or sequentially. Subject  802  may be prompted to select a pattern from the patterns presented. Computer system  811  may store the selection and subsequently present patterns according to the subject&#39;s selection. The patterns may be presented at least partially within the distortion region to assist subject  802  to determine the extent of distortion without having to shift the fixation of eye  803 . 
     In some embodiments, subject  802  may be able to vary aspects of patterns directly; for example, subject  802  may select a line thickness and/or an indicia size (and/or shape, color, and/or other aspects of a pattern) via input device  813 . In some embodiments, patterns are predetermined and/or dynamically generated and presented to subject  802  for selection. In some embodiments, subject  802  may provide a selection to an operator of computer system  811  and the operator may input the selection into computer system  811 . 
     As noted above, various patterns are presented to subject  802  during method  700 , including during calibration method  710 , reference pattern generation method  730 , and/or distortion mapping method  750 . Patterns may be displayed differently depending on the part of the retina by which they are likely to be perceived. For example, indicia may be presented in smaller sizes in higher-resolution areas of the visual field (the varying acuity of the retina is discussed above, with reference to  FIGS. 2A, 2B and 2C ). It is generally preferable for the granularity (i.e. resolution) of the pattern in a given location to generally correspond to the acuity of the corresponding portion of the retina (i.e. the portion of the retina on which the image of the pattern falls). The pattern may be presented as a grid divided into a plurality of portions with different resolutions generally corresponding to the acuity of the corresponding portions of the retina. Any number of different portions (and therefore different resolutions) may be provided. In some embodiments, three portions are provided, as discussed further below in reference to  FIG. 10A . 
       FIG. 10A  shows an example multi-resolution grid  1000 A. Multi-resolution grid  1000 A comprises a low-resolution portion  1010  (indicated by sparse grid lines  1012 ) on the periphery, a medium-resolution portion  1020  (indicated by relatively more dense grid lines  1022 ), and a high-resolution portion  1030  (indicated by significantly more dense grid lines  1032 ). In the depicted example, portions  1010 ,  1020 ,  1030  are concentric and centered on fixation target  1004 . Each portion  1010 ,  1020 ,  1030  may comprise a plurality of points (e.g. located at the intersections of grid lines  1012 ,  1022 , and  1032 ). As will be discussed in greater detail below, subject  802  may adjust patterns based on these points. 
     Grid lines  1012 ,  1022 , and  1032  are provided to better understand multi-resolution grid  1000 A, and are not necessarily displayed to subject  802 . Each intersection of grid lines  1012 ,  1022 , and  1032  may correspond to a point in a distortion map. Thus, the distortion map is of higher resolution near to the center of vision of subject  802  (which has greater visual acuity, as illustrated in  FIG. 2B ), and lower resolution towards the periphery (which has lesser visual acuity, as illustrated in  FIG. 2B ). In some embodiments, portions  1010 ,  1020 , and/or  1030  are sized to correspond to be angular sizes of macula  204 , the fovea  206 , and foveola  208 , respectively. For example, portion  1030  may have an angular diameter (or, more particularly in the case of the depicted square portion  1030 , an angular side-length) of approximately 1°, portion  1020  may have an angular diameter of approximately 6°, and portion  1010  may have an angular diameter in excess of 20°. 
     In some embodiments, portions  1010 ,  1020 , and/or  1030  may be differently sized and/or differently shaped. For example, portions  1020  and/or  1030  may be circular, elliptical, or otherwise shaped. In general, the preferred size of a particular portion will depend on the acuity of the corresponding part of the retina and on the size of the portion. A portion of the pattern which is much higher-resolution than its corresponding portion of the retina may impose a burden on the subject (since the excess resolution is “wasted” and requires additional and unnecessary attention from the subject), whereas a portion of the patter which is much lower-resolution than its corresponding portion of the retina may result in small distortions (e.g. located entirely between grid lines  1012 ) remaining undetected and thus uncorrected. 
       FIG. 10B  shows an example multi-resolution grid  1000 B with substantially the same features as multi-resolution grid  1000 A and patterns overlaid thereon. In particular, a low-resolution pattern  1018  (comprising large indicia  1014  and corresponding line  1016 ) is overlaid on low-resolution portion  1010 , a medium-resolution pattern  1028  (comprising medium indicia  1024  and corresponding line  1026 ) is at least partially overlaid on medium-resolution portion  1020 , and a high-resolution pattern  1038  (comprising small indicia  1034  and corresponding line  1036 ) is at least partially overlaid on high-resolution portion  1030 . 
     As depicted, each portion  1010 ,  1020 ,  1030  has an associated representation for indicia and/or lines therein. In some embodiments, including the depicted embodiment, patterns passing through high-resolution portion  1030  may be represented according to the representation associated with high-resolution portion  1030  even outside of high-resolution portion  1030 . Patterns passing through medium-resolution portion  1020  and not high-resolution portion  1030  may be represented according to the representation associated with medium-resolution portion  1020 . In some alternative embodiments, a particular pattern may be represented according to multiple representations; for example, a pattern may comprise small indicia  1036  within high-resolution portion  1030  and medium indicia  1026  within medium resolution portion  1020 . 
     In some embodiments, including the depicted embodiment, patterns  1018 ,  1028 ,  1038  comprise lines  1016 ,  1026 ,  1036 , respectively. Lines  1016 ,  1026 ,  1036  may assist subject  802  in assessing the straightness of the associated array of indicia  1014 ,  1044 ,  1034 . In some embodiments, lines  1016 ,  1026 ,  1036  are thin relative to their associated indicia  1014 ,  1024 ,  1034 . For example, each line  1016 ,  1026 ,  1036  may comprise a thickness not exceeding 20% of a diameter of the associated indicia  1014 ,  1024 ,  1034 . Lines  1016 ,  1026 ,  1036  may visually connect their associated indicia  1014 ,  1024 ,  1034 , e.g. by running through the centers of their associated indicia  1014 ,  1024 ,  1034 . In some embodiments, lines  1016 ,  1026 ,  1036  are a different color than their associated indicia  1014 ,  1024 ,  1034 . 
     Returning to  FIG. 7 , block  718  involves selecting a type of temporal variation for the selected patterns. Peripheral indicia (i.e. indicia perceived in the periphery of subject  802 &#39;s retina) may appear to fade over time due to a phenomenon known as the Troxler effect. It is desirable to prevent or delay the fading of peripheral indicia in order to enable subject  802  to use peripheral indicia as reference points. Causing peripheral indicia to move or otherwise vary in appearance over time may prevent or delay the fading of peripheral indicia. The particular style of variation most suitable to ameliorating the Troxler effect without being unduly distracting may vary from subject to subject. Accordingly, subject  802  may be presented with several styles of variation, simultaneously and/or sequentially. Subject  802  may be prompted to select a style of variation from those presented. Computer system  811  may store the selection and subsequently present patterns with the selected style of variation. 
     In some embodiments, only indicia which are at least 7° removed from the fixation target (i.e. indicia positioned at at least 7° retinal eccentricity) are made to vary in appearance in the selected manner. In some embodiments, indicia must also, or alternatively, be outside of the displacement region in order to vary in appearance in the selected manner. For example, in some embodiments, only indicia which are at least 7° removed from the fixation target and which are also at least 7° removed from the boundary of the displacement region may be made to vary in appearance in the selected manner. 
     A variety of variations are possible. A particular variation type which the inventors have found to give good results in some circumstances is movement of indicia (such as indicia  1014  in  FIG. 10B ) in the direction of their associated line (e.g. along line  1016  in  FIG. 10B ) once roughly every 5 seconds, alternating between movement in one direction (e.g. left) and the opposing direction (e.g. right). The indicia may move by, for example, half the distance between indicia. Movement may be substantially instantaneous (i.e. indicia may be stationary for 5 seconds, change location between frames and/or between refresh cycles of display  810 , and remain stationary for another 5 second before changing location again). Alternatively, or in addition, movement may be animated over a period of time. 
     Other types of variation are possible. For example, indicia may shift, bounce, stretch, rotate, pulse, grow, shrink, change color, and/or otherwise change their location or appearance. Indicia may move along a path other than (or in addition to) their associated lines, or may move in place (e.g. via rotation). 
     Calibration method  710  may comprise some or all of the above-identified blocks  712 ,  714 ,  716 ,  718 . In some embodiments, certain steps may be omitted or performed in a different order. For example, the block  718  selection of a pattern variation may not be performed, or may be performed before or in parallel with the block  716  selection of a pattern representation. Similarly, the block  716  selection of a pattern presentation may not be performed in some embodiments (e.g. the pattern representation may be predetermined) or may be performed before or in parallel with one or more of block  712  and  714 . 
     Once calibration method  710  is complete, method  700  may continue to reference pattern generation method  730 . Block  732  involves generating an initial reference pattern. The initial reference pattern passes through the distortion region and is adjusted by subject  802  so that the perception by subject  802  of the reference pattern is non-distorted. The initial reference pattern will appear distorted to an observer with a normal retina. The process of block  732  is illustrated in  FIGS. 11A, 11B, 11C, 11D, 11D, and 11F  (collectively and individually,  FIG. 11 ). 
       FIG. 11A  shows an example adjustment display  1102 A having a fixation target  1104  and a distortion region  1106  (distortion region  1106  may be, but is not necessarily, displayed to subject  802 ). A pattern  1110  passes through distortion region  1106 ; pattern  1110  comprises indicia and a line substantially as described above. 
     Pattern  1110  passes through a point  1108 . Indicia is displayed at point  1108 . In some embodiments, including in the depicted embodiment, point  1108  is the point within distortion region  1106  which is nearest to (is among the points nearest to) fixation target  1104 . Pattern  1110  passes through point  1108  in a particular direction (e.g. horizontally). Note that point  1108  may be, but is not necessarily, on the boundary of distortion region  1106 . In circumstances where fixation target  1104  is located inside distortion region  1106 , point  1108  may be located at fixation target  1104 . In such circumstances, fixation target  1104  may be represented by indicia which differ from the indicia of pattern  1110 ; for example, where pattern  1110  comprises several dots, fixation target  1104  may be represented by a crosshair (and/or an “X”). 
     Portions of pattern  1110  lying within distortion region  1106  may appear distorted to subject  802 . Subject  802  may select particular indicia of pattern  1110  and move the indicia until pattern  1110  appears non-distorted. In the case of a pattern  1110  which comprises a straight line, subject  802  may move the indicia of pattern  1110  until the resulting pattern appear straight. Subject  802  may move the indicia by providing inputs to input device  813 , substantially as described above. In some embodiments, computer system  811  allows subject  802  to move indicia within distortion region  1106  but does not permit subject  802  to move indicia outside of distortion region  1106 . This restriction may, in some circumstances, prevent subject  802  from introducing certain errors into the distortion map as illustrated, for example, in  FIGS. 5A, 5B, and 5C . Subject  802  may be further restricted to moving indicia in a direction orthogonal to pattern  1110  (e.g. vertically). 
       FIG. 11B  shows an example adjustment display  1102 B having an adjusted pattern  1120 . Adjusted pattern  1120  corresponds to pattern  1110  after subject  802  has moved indicia so as to cause pattern  1120  to be perceived as straight while eye  803  of subject  802  is fixed at fixation target  1104 . For example, the indicia formerly at point  1108  is now located at position  1118  (which may or may not be located at a point defined by the multi-resolution grid). As noted above, pattern  1110  (and, therefore, pattern  1120 ) may be placed near to fixation target  1104 ; in some circumstances, such a placement may cause subject  802  to be less likely to break fixation with fixation target  1104 . 
       FIG. 11C  shows an example adjustment display  1102 C having a pattern  1130  orthogonal to pattern  1110  (in this example, vertically). Pattern  1130  passes through point  1118 . In some embodiments, any adjustment to point  1108  (resulting in point  1118 ) may be reflected in pattern  1130 ; for example, as depicted, point  1118  is slightly displaced, as in  FIG. 11B . As described above, subject  802  may adjust indicia in pattern  1130  within distortion region  1106  to make pattern  1130  appear non-distorted (in this example, straight), thereby generating adjusted pattern  1140  shown in  FIG. 11D . Adjusted pattern  1140  comprises a point  1128  corresponding to point  1118  after adjustment by subject  802 . Subject  802  may be restricted when making adjustments as described above with reference to adjusted pattern  1120 . 
     Once patterns  1120  and  1140  have been determined, an initial reference pattern may be generated.  FIG. 11E  shows an example display  1102 E having an example initial reference pattern  1150  based on adjusted patterns  1120  and  1140 . Initial reference pattern  1150  comprises a reference pattern segment  1150 A which conforms to the shape of adjusted pattern  1120  (e.g. segment  1150 A is coincident with the centers of each of the indicia of adjusted pattern  1120 ), and a reference pattern segment  1150 B which conforms to the shape of adjusted pattern  1140  (e.g. segment  1150 B may be coincident with the centers of each of the indicia of adjusted pattern  1140 ). 
     Although initial reference pattern  1150  may appear distorted to a person with normal vision, metamorphopsia-affected subject  802  may have perception  1102 F as shown in  FIG. 11F . That is, subject  802  may perceive initial reference pattern  1150  as a non-distorted perceived pattern  1160 . In the depicted example, perceived pattern  1160  comprises segments  1160 A and  1160 B corresponding to segments  1150 A and  1150 B, respectively, each of which appears straight to subject  802  when eye  803  of subject  802  is fixed on fixation target  1104 , provided that subject  802 &#39;s head is similarly in registration with display  810 . 
     In some embodiments, segments  1150 A and  1150 B comprise distorted lines which have different thicknesses than the lines of patterns  1120  and  1140 . For example, segments  1150 A and  1150 B may be approximately 50% thicker than segments  1150 A and  1150 B. A thickness may be selected based on the subject&#39;s preference; for example, a thickness which the subject reports to be relatively less distracting may be selected. By changing the thickness of segments  1150 A and  1150 B relative to patterns  1120  and  1140 , pattern  1150  is made visually distinct from subsequently-displayed patterns (discussed further below). 
     Although it is possible to provide as many indicia as there are photoreceptors along a given pattern  1120  or  1140 , this is rarely practical (since subject  820  would need to adjust potentially tens of millions of indicia). Accordingly, it is generally advantageous to provide a smaller number of indicia in each pattern  1120  and  1140 , e.g. in the range from 40 to 60 indicia. A larger number of indicia may be provided when appropriate in the circumstances, such as where greater granularity is required for research purposes, where the distortion region is located around or near to the fovea, where the results of the distortion mapping are intended for use in the calibration of a corrective device with greater granularity, or in other circumstances. For example, the number of indicia may be selected by subject  802  and/or an operator of system  800 . The number of indicia may be determined according to the resolution region on which the representation of patterns  1120  and  1140  are based—for example, patterns displayed based on the representation associated with the low-resolution region  1010  may have fewer indicia than those displayed based on the representation associated with the low-resolution regions  1020  and  1030  (as shown, for example, in  FIG. 10 ). 
     Accordingly, it is generally necessary to derive the locations of portions of segments  1150 A and  1150 B which are located between the coordinates of the indicia of patterns  1120  and  1140 . This derivation may be performed by interpolation. Any suitable interpolation algorithm may be used for this derivation. In some embodiments, Bezier curves and/or splines are used to interpolate the locations of segments  1120  and  1140  between the coordinates provided by the indicia of patterns  1120  and  1140  within distortion region  1106 . 
     Returning to  FIG. 7 , once initial reference pattern  1150  has been generated, it may be tested at block  734 . Such testing may comprise displaying pattern  1150  to subject  802  and confirming whether the pattern appears non-distorted (e.g. as shown in perception  1102 F of  FIG. 11F ) when subject  802  fixes eye  803  on fixation target  1104  and has his/her head in registration with display  810 . Computer system  811  may provide a prompt for such confirmation to subject  802  via display  810 , via another device, or via an operator of system  811  (e.g. system  811  may prompt the operator to ask subject  811 ). Subject  802  and/or an operator may provide an input to computer system  811  to indicate whether perceived pattern  1160  appears non-distorted or not. 
     It may not be necessary, in some circumstances, for subject  802  to perceive pattern  1150  as completely non-distorted. It may be sufficient for perceived pattern  1160  to sufficiently approximate a non-distorted pattern. Accordingly, computer system  811  does not require any particular level of perceived distortion (and, in any event, would likely not be capable of enforcing such a requirement using present technology), but rather receives an indication that the reference pattern either passes or fails to pass the test of block  734 . 
     If computer system  811  receives input which corresponds to a pass (e.g. indicating a substantially non-distorted pattern  1160 ), method  700  may proceed to block  752  of distortion mapping method  750 . Otherwise, if computer system  811  receives input which corresponds to a fail (e.g. indicating a distorted pattern  1160 ), method  700  may proceed to block  736  of reference pattern generation method  730 . 
     Block  736  involves displaying one or both of adjusted patterns  1120  and  1140  to subject  802  and permitting subject  802  to further adjust patterns  1120  and  1140  substantially as described above. Adjusted patterns  1120  and  1140  may be displayed sequentially and/or simultaneously. If adjusted patterns  1120  and  1140  are displayed simultaneously, subject  802  may be permitted to adjust their point of commonality (i.e. point  1128 ) in any permitted direction, but adjustments to other points may continue to be restricted as discussed above. Method  700  (and thus method  730 ) returns to block  734  to repeat the testing of the resulting reference pattern, as described above. 
     As discussed above, there may be various points within distortion region  1106  (e.g. corresponding to intersections of grid lines  1012 ,  1024 ,  1034  on multi-resolution grid  1000 A of  FIG. 10A ), some of which correspond to points on pre-adjustment patterns  1110  and  1130 . Method  750  involves generating adjusted patterns for each point in the distortion region (e.g. distortion region  1106 ) so that each point is associated with each required type of adjusted pattern. For example, computer system  811  may require that each point be associated with a first linear pattern in a given direction and a second linear pattern in an orthogonal direction. For instance, in the depicted examples both horizontal and vertical patterns are used, so method  750  may involve generating horizontal and/or vertical adjusted patterns for each point in region  1106  which is not yet associated with horizontal and/or vertical adjusted patterns. Other types of adjusted patterns may alternatively, or additionally, be used; for example, method  750  may also, or alternatively, require that each point be associated with a diagonal linear pattern, with a non-linear (e.g. circular or elliptical) pattern, or with any other suitable type of pattern. 
     In the depicted example of  FIG. 11 , point  1128  is the only point which has corresponding vertical and horizontal adjusted patterns. Other points along adjusted pattern  1120  have only a corresponding horizontal adjusted pattern, so method  750  may involve generating vertical adjusted patterns for each of those points (and similarly generating horizontal adjusted patterns for each of the points other than point  1128  along adjusted pattern  1140 ). Method  750  may involve generating both vertical and horizontal adjusted patterns for each remaining point in distortion region  1106  which is not located along either of adjusted patterns  1120  or  1140  (or their pre-adjustment counterparts, patterns  1110  and  1130 ). 
     Accordingly, block  752  involves determining whether additional patterns remain to be displayed to (and adjusted by) subject  802  in distortion region  1106 . In some embodiments, including the depicted example, this determination comprises determining whether any points within distortion region  1106  do not yet have corresponding adjusted patterns of a required type (e.g. horizontal or vertical). For example,  FIG. 12A  shows an example point  1204  which is already associated with horizontal adjusted pattern  1140 , but is not yet associated with a vertical pattern (which, in this example, is required).  FIG. 12A  is discussed in greater detail below. 
     Having identified a point which requires an additional adjusted pattern, method  700  (and therefore method  750 ) may proceed to block  754 . Block  754  involves displaying further patterns to subject  802 , similar in some respects to the display of patterns discussed above (e.g. shown in  FIG. 11 ). An example of such a display  1202 A is shown in  FIG. 12A . Display  1202 A has a point  1204  and an additional pattern  1202  which includes point  1204 . Note that point  1204  may be positioned according to previous adjustments which have included it, and not necessarily along gridlines  1012 ,  1022 , or  1032 . Subject  802  may adjust indicia along pattern  1202  to generate adjusted pattern  1206 , as shown in display  1202 B of  FIG. 12B . This adjustment may be performed similarly to (and subject to the same constraints as) the adjustment of patterns  1110  and  1130 , as discussed above. 
     In the example depicted, point  1204  only requires pattern  1202 ; in some circumstances, a given point may require multiple additional patterns, each of which may be generated by block  754  substantially as described above (e.g. with reference to block  732 ). That is, block  754  may generate multiple patterns corresponding to the given point sequentially and/or in parallel. In some alternative embodiments, block  754  may generate only one pattern for a given point, and may generate additional patterns for the given point (if necessary) on subsequent iterations. 
     In addition to pattern  1202 , display  1202 A (and/or display  1202 B) may also include reference pattern  1140 . Reference pattern  1150  may assist subject  802  in ensuring that the head of subject  802  remains in registration with display  810 . As described above, if subject  802  fixates eye  803  on fixation point  1104  and keeps his or her head in registration with display  810 , reference pattern  1150  should appear substantially non-distorted. Effectively, reference pattern  1150  may provide a mechanism by which subject  802 &#39;s visual distortions may be used to assist in avoiding common errors in the distortion mapping process, since movements of subject  802 &#39;s head or eye  802  may result in reference pattern  1150  appearing distorted. 
     Method  700  (and therefore method  750 ) may proceed to block  756 , which involves testing adjusted pattern  1206  to determine whether adjusted pattern  1206  appears non-distorted (or substantially non-distorted) to subject  802 . Such testing may comprise displaying adjusted pattern  1206  to subject  802  and confirming whether the pattern appears non-distorted, as described above with reference to block  736  of method  730 . However, block  756  may also involve displaying reference pattern  1150  to subject  802  and confirming that both reference pattern  1150  and adjusted pattern  1206  appear non-distorted. If adjusted pattern  1206  appears non-distorted but reference pattern  1150  appears distorted, it can be concluded that subject  802 &#39;s eye  803  or head is out of registration with display  810  or fixation target  1104  and that the block  756  test should be repeated (or simply continued, since an input to computer system  811  may not be necessary until a pass or fail has been determined). 
     If computer system  811  receives input which corresponds to a pass (e.g. indicating a substantially non-distorted pattern  1206  and reference pattern  1150 ), method  700  may proceed to block  752  of distortion mapping method  750 . Otherwise, if computer system  811  receives input which corresponds to a fail (e.g. indicating a distorted pattern  1206  while reference pattern  1150  appears non-distorted), method  700  may proceed to block  758 . 
     Block  758  involves displaying one or more of the adjusted patterns generated by block  754  (e.g. adjusted pattern  1206 ) to subject  802  and permitting subject  802  to further adjust the pattern(s) substantially as described above with reference to block  736 . As with block  754 , reference pattern  1150  may be displayed during the further adjustment of the pattern(s). Method  700  (and thus method  750 ) returns to block  756  to repeat the testing of the resulting adjusted patterns, as described above. 
     Once all of the points in distortion region  1106  have corresponding adjusted patterns of the required types, method  700  may proceed to perception map generation method  770 , and in particular to block  772 . Block  772  involves generating a distortion map from the adjusted patterns generated by methods  730  and/or  750  (such as reference pattern  1150  and adjusted pattern  1206 ). The union of the adjusted patterns may provide a grid with distorted lines which, when viewed by subject  810  while fixating eye  803  on fixation target  1104  and with the head of subject  802  in registration with display  810 , appears substantially non-distorted. These grid lines provide a map from “normal” visual space to “corrected” visual space. For example, if point  1128  corresponds to point  1108  prior to subject  802 &#39;s adjustments, then the coordinates of point  1108  may be mapped to the coordinates of point  1128 . 
     For example, if point  1108  has coordinates of ( 100 ,  100 ) relative to fixation target  1104  (in (X,Y) coordinate format), and if point  1128  has coordinates of ( 110 ,  105 ) in the same format, then an image may be mapped from “normal” visual space to “corrected” visual space by mapping elements (e.g. pixels) of an image located at ( 100 ,  100 ) to the new location ( 110 ,  105 ). If all elements along pre-adjustment patterns  1110 ,  1130 ,  1202 , etc. (including elements along the lines thereof) are mapped to the corresponding coordinates along adjusted patterns  1120 ,  1140 ,  1206 , etc. (based on the above-described interpolated lines), then the “corrected” image may appear non-distorted to subject  802  along at least the perceived areas corresponding to adjusted patterns  1120 ,  1140 ,  1206 , etc. (although those areas may still appear distorted if neighbouring areas are distorted, due to the complexities of cognitive processing). 
     Accordingly, a partial distortion map may be generated by mapping coordinates of all pre-adjustment patterns (such as patterns  1110 ,  1130 ,  1202 , etc.) to the corresponding coordinates along adjusted patterns  1120 ,  1140 ,  1206 , etc. However, in many circumstances it is desirable to generate a more detailed distortion map which also maps locations not on patterns  1110 ,  1130 ,  1202 , etc. to locations not on adjusted patterns  1120 ,  1140 ,  1206 , etc. 
     Method  770  (and in particular block  772 ) may involve mapping such coordinates by interpolation. For example, coordinates within distortion grid  1106  may be mapped from “normal” visual space to “corrected” visual space by applying bicubic interpolation based on the partial distortion map. Thus, each coordinate in “normal” visual space not already mapped to a coordinate in “corrected” visual space by the partial distortion map may be mapped to such a coordinate based on the mappings of the surrounding coordinates (in “normal” visual space). The mapped coordinates may be included in the generated distortion map. Other types of interpolation may be used. Preferably, two-dimensional interpolation methods may be used, such as bilinear interpolation, bicubic interpolation, Bèzier surfaces, and/or other interpolation methods. 
     Once a distortion map has been generated, method  700  (and therefore method  770 ) may optionally proceed to block  774 , which involves validating the distortion map generated at block  772  to confirm that the generated distortion map is sufficiently accurate; that is, to confirm that images mapped from “normal” space to “corrected” space by applying the distortion map are perceived by subject  802  as substantially non-distorted. This validation may comprise displaying a validation pattern. 
       FIG. 13A  shows an example validation pattern  1300 A having a fixation target  1304  and grid lines  1302 . Grid lines  1302  do not necessarily correspond to grid lines  1012 ,  1022 ,  1032  of grid  1000 A. An area  1306  has been distorted according to the distortion map so that all grid lines  1302  should be perceived as straight by subject  802 . For instance, validation pattern  1300 A may comprise a conventional Amsler grid which has been distorted according to the distortion map. Alternatively, or in addition, other validation patterns such as other patterns, photographs, or other images may be displayed to subject  802 . 
     Block  774  may comprise varying the displayed validation patterns. For example, block  774  may comprise rotating the validation pattern, updating the distorted area  1306  to reflect any movement or other change in the underlying pattern. For example, the Amsler grid of  FIG. 13A  may be rotated about fixation point  1304  through 90°.  FIG. 13B  shows an example validation pattern  1300 B which corresponds to the Amsler grid of  FIG. 13A  rotated 45°, with the distortion map applied in area  1306  to distort the grid lines of the rotated grid according to the distortion map (which is not rotated with the validation pattern). Other validation patterns, such as those with a different degree of rotational symmetry, may be rotated more or less—for instance, a validation pattern without rotational symmetry may be rotated through a full 360°. Reference pattern  1150  may be displayed during the display of validation patterns  1300 A,  1300 B, as described above. 
     As with blocks  734  and  736 , computer system  811  may receive an input indicating whether the validation passes or fails—e.g. if subject  802  perceives a distortion during the rotation of validation patterns  1300 A,  1300 B, then computer system  811  may be provided with an input which indicates failure. In response to receiving an input indicating that the validation passes, method  700  (and therefore method  770 ) may proceed to block  776 . Otherwise, if the computer system  811  receives an input indicating that the validation fails, block  774  may involve further refinement of the distortion map, as described below. 
     If a portion of a validation pattern is perceived by subject  802  to be distorted, a failure indication may be provided to computer system  811 . Subject  802  may then select a region of the validation pattern which appears distorted and make further adjustments. For example,  FIG. 14A  shows an example perception  1400 A of a selection display showing a perceived portion  1402  of validation pattern  1300 B. Portion  1402  generally corresponds to area  1306 . Area  1404  has distorted according to the distortion map (and so should, ideally, appear non-distorted), but subject  802  nevertheless perceives area  1404  as distorted. Subject  802  may select a point where a distortion is perceived. In this example, subject  802  has selected (e.g. via input device  813 ) point  1406  in area  1404 . Reference pattern  1150  (not shown) and/or fixation target  1106  (not shown) may continue to be displayed as described above. 
     In some embodiments, a guide pattern  1408  may be displayed to subject  802  to assist subject  802  in selecting a point. For example, guide pattern  1408  may comprise a crosshair which has been distorted according to the distortion map. Guide pattern  1408  may be displayed instead of, or in addition to, a user interface element such as a mouse cursor. Subject  802  may move the intersection of the crosshair to point  1406  (or to any other point in the distortion region) and select point  1406  using input device  813  or any other means. Guide pattern  1408  may be easier for subject  802  to identify than non-distorted user interface elements in areas where the distortion map is accurate. In some embodiments and in some circumstances, guide pattern  1408  may assist subject  802  in identifying areas where the distortion map is inaccurate by essentially providing a dynamic reference pattern in areas of interest. For example, as shown in  FIG. 14A , guide pattern  1408  is perceived as distorted in area  1404 . 
     In some embodiments, guide pattern  1408  comprises lines which are thinner than the lines of patterns  1110  or  1130 . For example, guide pattern  1408  may comprise lines which are less than half as thick as the lines of patterns  1110  or  1130 . Guide pattern  1408  may also, or alternatively, be in a different colour than the lines of patterns  1110  or  1130  and/or validation pattern  1402 . 
     Once point  1406  has been selected, a refinement display  1400 B may be displayed to subject  802 , as shown in  FIG. 14B . Refinement display  1400 B may include point  1406  and/or interpolated pattern  1418 . Interpolated pattern  1418  may be substantially similar to guide pattern  1408 . For example, interpolated pattern  1418  may comprise a crosshair which has been distorted according to the distortion map. The distortion map may comprise grid lines  1410 , which are not necessarily shown to subject  802 . Grid lines  1410  may comprise adjusted patterns  1120 ,  1140 ,  1206 , etc. Anchor points  1412  may be placed at the points where interpolated pattern  1418  intersects with grid lines  1410 . Interpolated pattern  1418  may be derived from the distortion map, the interpolation of which is described above. In some embodiments, multiple interpolated patterns  1418  may be displayed to the subject; each interpolated pattern  1418  may be generated using a different interpolation algorithm. For example, one interpolated pattern  1418  may be generated using bilinear interpolation, another using bicubic interpolation, another using Bezier surfaces, and so on. The subject may select any one of the presented interpolated patterns  1418  for use by system  800 ; the selected interpolated pattern  1418  may be further refined as discussed below. 
       FIG. 14C  shows an example perception  1400 C of display  1400 B by subject  802 . Grid lines  1420  correspond to distorted grid lines  1410 . Although grid lines  1420  are not necessarily visible to subject  802 , if they were visible they would likely be perceived to be straight (since they correspond to previously-tested adjusted patterns  1120 ,  1140 ,  1206 , etc.). Perceived pattern  1428  is subject  802 &#39;s perception of interpolated pattern  1418 . Subject  802  perceives a distortion in perceived pattern  1428 , as is clearly visible in  FIG. 14C . 
     Subject  802  may be permitted to adjust the position of point  1406  so that interpolated pattern  1418  appears substantially non-distorted at least in the area bounded by anchor points  1412 . Adjustment of the position of point  1406  may be performed substantially as described above with reference to blocks  736 ,  754  and points  1128  and  1204 . Further points along interpolated pattern  1418  between point  1406  and anchor points  1412  may be defined and may be adjusted by subject  802 . In response to an adjustment of the position of point  1406  (and/or other points) by subject  802 , computer system  811  may reinterpolate portions of pattern  1418 . In some embodiments, only the portions of pattern  1418  which are bounded by anchor points  1412  are reinterpolated (i.e. the effects of adjustments may be confined to the cell defined by grid lines  1410  in which the adjustment occurs). 
     The resulting adjusted and/or reinterpolated pattern may, optionally, be tested substantially as described with reference to block  756  and, if computer system  811  receives an input indicating that the test is passed, the reinterpolated pattern may be incorporated into the distortion map as if it were an adjusted pattern  1120 ,  1140 ,  1206 , etc. Coordinates surrounding the reinterpolated and/or adjusted pattern may be used as a basis for further reinterpolation of the distortion map. For example, coordinates not on the reinterpolated pattern but within the area bounded by grid lines  1410  on which anchor points  1412  are defined may have their mappings reinterpolated. 
     Validation pattern  1402  need not necessarily displayed to subject  802  during refinement of interpolated pattern  1418 . Reference pattern  1150  (not shown) and/or fixation target  1106  (not shown) may continue to be displayed as described above. 
     Once generated (and optionally validated and/or refined), a distortion map may be used for various purposes. For example, a distortion map may be used to generate corrective optics, such as shaped lenses, GRIN lenses, and the like. As another example, distortion maps may be used to generate corrective displays, such as HUDs with eye trackers, adaptive vision goggles, video displays, and the like. As a further example, distortion maps may be used to generate quantitative measures of the physical displacement of the retina of a subject  802 , which may assist in researching and/or treating metamorphopsia. 
     In some embodiments, after generating a distortion map at block  772  (and/or, optionally, after validating the distortion map at block  774 ), method  700  proceeds to block  776 , which involves generating a perception map. Unlike a distortion map, which allows for a mapping of “normal” images to “corrected” images which are perceived as substantially non-distorted by subject  802 , a perception map enables a person with normal vision to perceive distortions substantially as they are perceived by metamorphopsia-affected subject  802 . 
     As illustrated, for example, by  FIGS. 4B and 6A , a perception map is not necessarily the same as the geometric inverse of a distortion map. For instance, at the  0  index along axis  306 , perceived line  412  is offset from the position of line  302  by −1 unit, but the geometric inverse of line  604  at the same location would result in an offset of −2 units. 
     The block  776  generation of a perception map may involve finding a functional inverse of the distortion map. That is, given a distortion map D: N→C, where N is the “normal” visual space and C is the “corrected” visual space which complements the distortion of subject  802 , and given that D (I) for an arbitrary image I is perceived by subject  802  as substantially non-distorted, then the perception map P: C→N can be defined as P(I)=D − (I), so that P(D(I))=I. In other words, given a coordinate pair (x,y) such that D((x,y))=(x′,y′), the perception map can be defined as P((x′,y′))=(x,y). 
     In some embodiments, computer system  811  stores the distortion map at least partially as a lookup table, and generates the perception map by performing a reverse lookup and/or by reversing the lookup table. 
     Once generated, a perception map may be used for various purposes. For example, a perception map may be used as a tool by those who work with metamorphopsia-affected individuals as part of a treatment, rehabilitation, and/or the like. As another example, a perception map may be used to determine a quantitative measure of the visual distortions perceived by a subject  802 , which may be relevant to assessing the overall quality of vision (and/or quality of life) of a subject  802 . Quantitative measures may also, or alternatively, be generated from distortion maps; although a perception map may better approximate the subjective distortions perceived by a subject  802 , it may be convenient or desirable in some circumstances to generate quantitative measures from a distortion map. System  811  may provide one or more quantitative measures of the visual distortions perceived by subject  802 . Certain methods of determining quantitative measures are discussed below, with example methods illustrated in  FIGS. 15A, 15B, 15C, and 15D . 
     In some embodiments, system  811  may determine a quantitative measure based on an area of the distortion region identified by subject  802  (e.g. distortion region  950 ,  960 , and/or  970  of  FIGS. 9J, 9K, and 9L ).  FIG. 15A  shows an example map  1500  (which, as discussed above, may be a perception map or a distortion map). Grid lines  1502  are shown for the sake of clarity, although, as discussed above, the distortion and perception maps may be interpolated to provide a mapping which includes points not located on grid lines  1502 . Subject  802  has identified boundary lines  1504  which contain the distortion region, as described above. A quantitative measure Q may be determined based on the area of the distortion region, e.g. so that distortion regions with larger areas may correspond to quantitative measures reflecting more severe distortions. 
     Due to the physiological nature of metamorphopsia, the actual distortion perceived by subject  802  is unlikely to be bounded by straight lines. Most commonly (although not universally), the actual distortion perceived by subject  802  is likely to be better-approximated by an ellipse than by a linearly bounded distortion region. System  811  may determine an ellipse  1506  which approximates the distortion region, and may determine a quantitative measure based on the area of ellipse  1506 . In some embodiments, ellipse  1506  may be bounded by the distortion region identified by subject  802 . For example, a quantitative measure Q may be determined according to the formula: 
         Q =ƒ(π× a×b )
 
     where a is the radius of the major axis of the ellipse, b is the radius of the minor axis of the ellipse, and ƒ is a function which takes the area of the ellipse as an input. ƒ may be the identity function. 
     In some embodiments, system  811  may determine the quantitative measure based on the severity of displacement of all or part of the distorted region.  FIGS. 15B, 15C and 15D  show an expanded view of a portion of example map  1500 , namely the portion in the vicinity of the distortion region. In some embodiments, system  811  selects a line  1514  as displayed at display  810  (i.e. prior to being perceived and distorted) passing through the distortion region. Line  1512  is the perception of line  1514  by subject  802 ; as shown, line  1512  is distorted so that various points therein are displaced relative to line  1514 . System  811  may determine a quantitative measure based on the severity of the displacement caused by this distortion. 
     In some embodiments, the severity of displacement may be determined based on an area displaced.  FIG. 15B  illustrates an example method for determining a severity of displacement based on an area displaced. System  811  may determine the severity (and thus the quantitative measure Q) based on the area  1516  between original line  1514  and distorted line  1512 . Such an area may be approximated, for example, by summing the displacement of indicia along line  1512  relative to line  1514 , by integrating along the curve of line  1512  (e.g. using numerical integration methods, such as Simpson&#39;s rule, and/or symbolic integration methods) to determine the approximate area between lines  1512  and  1514 , and/or by other methods. For example, a quantitative measure Q may be determined according to the formula: 
         Q =ƒ(∫ a   b   |g ( x )| dx )
 
     where a and b are points which bound the distorted portion of the linear cross-section (e.g. a and b may be on opposing sides of the boundary of the distorted region, on opposing sides of display  1202 B, or elsewhere), g(x) is the displacement of point x on the linear cross-section, and ƒ is a function which takes the area of displacement as an input. ƒ may be the identity function. 
     As another example, system  811  may determine the severity of the displacement based on a linear displacement of a particular point.  FIG. 15C  illustrates an example method for determining a severity of displacement based on the displacement of a point  1522  from its original (pre-distortion) position  1524 . For example, the severity of displacement at point  1522  may be determined based on the magnitude of the displacement distance  1526  from original position  1524  to the current position of point  1522 . For example, a quantitative measure Q may be determined according to the formula: 
         Q =ƒ(| g   a ( x )− g   b ( x )|)
 
     where g a (x) is the position of a point x after applying the distortion map, g b (x) is the position of the same point x in the original image (i.e. before applying the distortion map), and ƒ is a function which takes the displacement of a point as an input. ƒ may be the identity function. 
     As yet another example, system  811  may determine the severity of the displacement at a particular point based on a local change in displacement.  FIG. 15D  illustrates an example method for determining a severity of displacement based on the local change in displacement of point  1522 . The change in displacement at a particular point (e.g. point  1522 ) in a distorted image relative to nearby points can be a reasonable predictor of the severity of a subject&#39;s perceived distortion. That is, even if a point is severely displaced, if all surrounding points are similarly displaced then the subject may perceived relatively less distortion at that point. System  811  may determine a gradient (and/or an approximation thereof) over the distortion region, for example using vector analysis and/or numerical analysis methods. The gradient at a particular point is the rate of change in the point&#39;s displacement (as measured above) relative to nearby points, and/or instantaneously at that point. A quantitative measure Q for a particular point  1522  may be determined based on the gradient. 
     It may be convenient or otherwise desirable to approximate the local change in distortion for a particular point without necessarily conducting vector analysis on each point. The rate of change in displacement at a particular point  1522  (i.e. the approximated value of the gradient at point  1522 ) may be approximated based on the displacement distance  1526  (discussed above) and the inner distance  1536  between point  1522  and the boundary of the distortion region (e.g. at point  1532 ). Inner distance  1536  may be the distance from original position  1524  to boundary point  1532 , the distance from the projection of point  1522  onto line  1514  to boundary point  1532 , and/or some other distance which relates point  1522  to the boundary of the distortion region. Boundary point  1532  is the closest point to point  1522  on both the boundary of the distortion region and on line  1514  (or, equivalently in this example, line  1512 ). A quantitative measure may be determined by scaling the displacement distance  1526  by inner distance  1536  so that, if the displacement distances of points along line  1512  stay the same as their inner distances increase, the quantitative measure will reflect decreasing severity rather than uniform severity. 
     For example, a quantitative measure Q may be determined according to the formula: 
     
       
         
           
             Q 
             = 
             
               f 
                
               
                 ( 
                 
                   
                     
                       
                         g 
                         a 
                       
                        
                       
                         ( 
                         x 
                         ) 
                       
                     
                     - 
                     
                       
                         g 
                         b 
                       
                        
                       
                         ( 
                         x 
                         ) 
                       
                     
                   
                   
                     d 
                      
                     
                       ( 
                       x 
                       ) 
                     
                   
                 
                 ) 
               
             
           
         
       
     
     where g a (x) is the position of point x after applying the distortion map, g b (x) is the position of point x in the original image (i.e. before applying the distortion map), d(x) is the distance from the point x to the closest point on the boundary of the distortion region (e.g. inner distance  1536 ), and ƒ is a function which takes the displacement of a point as an input. ƒ may be the identity function. 
     In some embodiments, a quantitative measure Q may be based on the severity of the displacement of one or more points. For example, given a set of points P in the distortion region, the quantitative measure Q may be determined based on a statistical measure of the linear displacement and/or gradient of the points in P, such as (for example) the mean, median, mode, maximum, or other measure. Multiple quantitative measures Q may be determined by system  811 ; for instance, each point in P may be associated with its own quantitative measure, from which a “heat map” may be generated to assist in assessment of the severity of distortion in specific regions of the subject&#39;s vision. 
     Interpretation of Terms 
     Unless the context clearly requires otherwise, throughout the description and the
         “comprise”, “comprising”, and the like are to be construed in an inclusive sense, as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to”;   “connected”, “coupled”, or any variant thereof, means any connection or coupling, either direct or indirect, between two or more elements; the coupling or connection between the elements can be physical, logical, or a combination thereof;   “herein”, “above”, “below”, and words of similar import, when used to describe this specification, shall refer to this specification as a whole, and not to any particular portions of this specification;   “or”, in reference to a list of two or more items, covers all of the following interpretations of the word: any of the items in the list, all of the items in the list, and any combination of the items in the list;   the singular forms “a”, “an”, and “the” also include the meaning of any appropriate plural forms.       

     Words that indicate directions such as “vertical”, “transverse”, “horizontal”, “upward”, “downward”, “forward”, “backward”, “inward”, “outward”, “vertical”, “transverse”, “left”, “right”, “front”, “back”, “top”, “bottom”, “below”, “above”, “under”, and the like, used in this description and any accompanying claims (where present), depend on the specific orientation of the apparatus described and illustrated. The subject matter described herein may assume various alternative orientations. Accordingly, these directional terms are not strictly defined and should not be interpreted narrowly. 
     Specific examples of systems, methods and apparatus have been described herein for purposes of illustration. These are only examples. The technology provided herein can be applied to systems other than the example systems described above. Many alterations, modifications, additions, omissions, and permutations are possible within the practice of this invention. This invention includes variations on described embodiments that would be apparent to the skilled addressee, including variations obtained by: replacing features, elements and/or acts with equivalent features, elements and/or acts; mixing and matching of features, elements and/or acts from different embodiments; combining features, elements and/or acts from embodiments as described herein with features, elements and/or acts of other technology; and/or omitting combining features, elements and/or acts from described embodiments. 
     Computer system  811  and/or components thereof (including, for example, one or more processors) may comprise hardware, software, firmware or any combination thereof. Computer system  811  may comprise one or more microprocessors, digital signal processors, graphics processors, field programmable gate arrays, and/or the like. Components of computer system  811  may be combined or subdivided, and components of computer system  811  may comprise sub-components shared with other components of computer system  811 . Components of computer system  811  may be physically remote from one another. 
     Where a component is referred to above (e.g., a system, display, processor, etc.), unless otherwise indicated, reference to that component (including a reference to a “means”) should be interpreted as including as equivalents of that component any component which performs the function of the described component (i.e., that is functionally equivalent), including components which are not structurally equivalent to the disclosed structure which performs the function in the illustrated exemplary embodiments of the invention. 
     It is therefore intended that the following appended claims and claims hereafter introduced are interpreted to include all such modifications, permutations, additions, omissions, and sub-combinations as may reasonably be inferred. The scope of the claims should not be limited by the preferred embodiments set forth in the examples, but should be given the broadest interpretation consistent with the description as a whole.