Abstract:
The disclosure relates to a method for selecting progressive ophthalmic lenses for a given frame and wearer, the progressive ophthalmic lenses having one area for distance vision and one area for near vision, said given frame having two recesses suitable for receiving a progressive ophthalmic lens, respectively, said two recesses defining a recess midplane. The method includes the following steps: a) fitting said wearer with said given frame; b) determining the position of a first point of intersection between a first direction of the gaze of said wearer in a distance vision posture and said recess midplane; c) determining the position of a second point of intersection between the gaze of said wearer in a near vision posture and said recess midplane; d) assessing the distance between said intersection points; and, e) selecting progressive ophthalmic lenses in which the progression length corresponds to said distance assessed between said intersection points.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a 35 U.S.C. §371 National Phase conversion of PCT/FR2011/052215, filed Sep. 23, 2011, which claims benefit of French Application No. 1057684, filed Sep. 23, 2010, the disclosures of which are incorporated herein by reference. The PCT International Application was published in the French language. 
     BACKGROUND OF THE INVENTION 
     1. Technical Field 
     The present invention pertains to a method for selecting progressive ophthalmic lenses for a given frame fitted to a determined wearer. 
     2. Related Art 
     Progressive ophthalmic lenses are associated with a medical prescription and they are housed in a frame that the wearer chooses as a function of his tastes. 
     Lenses of this type exhibit a far vision zone, situated in the upper part of the lens and a near vision zone situated in the lower part. These vision zones exhibit different optical characteristics. Hence, and this is a particular feature of this type of ophthalmic lens, it exhibits a progression corridor which extends from one zone to the other, and whose optical characteristics vary in a continuous manner. Thus, from the far vision zone to the near vision zone, the optical characteristics of the far vision zone evolve progressively to the optical characteristics of the near vision zone. This allows the wearer to pass from one zone to the other without inconvenience and with a certain comfort. 
     However, this progression corridor and especially its length may vary from one frame to another. It is indeed understood that the progression length varies as a function of the position of the ophthalmic lenses with respect to the eye, and consequently with respect to the chosen frame. 
     Hence, it has been contemplated to take into account the size and the shape of the frame for the purposes of optimizing the progressive ophthalmic lens is brought to an optimal level of comfort for the wearer. It will be possible especially to refer to the document FR 2 898 193, which describes a procedure for determining a progressive ophthalmic lens suited to the wearer and to the chosen frame. 
     The procedure calls upon representative parameters obtained on the basis of mean values which are themselves calculated on the basis of a given population sample. Despite these precautions, it turns out that certain people experience difficulties in enduring their progressive ophthalmic lenses. 
     Hence, a problem which arises and which the present invention is intended to solve is to provide a method for selecting progressive ophthalmic lenses as a function of the characteristics of the wearer and of the frame that he chooses, so as to yet further increase his comfort of vision. 
     SUMMARY OF THE INVENTION 
     With this aim, the present invention proposes a method for selecting progressive ophthalmic lenses for a given frame and a given wearer, the progressive ophthalmic lenses exhibiting a far vision zone and a near vision zone spaced apart by a progression length, said given frame exhibiting two recesses able respectively to receive a progressive ophthalmic lens, said two recesses defining a recess mid-plane. According to the invention the method comprises the following steps: a) said given wearer is fitted with said given frame; b) the position of a first point of intersection of a first direction of gaze of said wearer in a far vision posture and of said recess mid-plane is determined with respect to said frame; the position of a second point of intersection of a second direction of gaze of said wearer in a near vision posture and of said recess mid-plane is determined with respect to said frame; the distance which extends between said points of intersection is evaluated; and, progressive ophthalmic lenses whose progression length corresponds to said evaluated distance between said points of intersection are selected. 
     Thus, a characteristic of the invention resides in the customized measurement of the relative positions of the points of intersection of the recess mid-plane, respectively with the directions of gaze of the wearer in far vision and in near vision and in the evaluation of the distance which separates these points of intersection so as to select corresponding progressive ophthalmic lenses. In practice, it is for example possible to tag respectively these points of intersection with respect to the lower edge of the frame and to measure vertically the distance which separates them therefrom. It turns out that the distance which separates these points of intersection differs from one patient to another and from one frame to another and does so in relatively significant proportions. Now, progressive ophthalmic lenses are offered with standard progression lengths which are not necessarily suited in all circumstances for a given wearer fitted with a given frame. By virtue of the method according to the invention, it is possible to choose for a given wearer who has chosen a frame the progressive ophthalmic lenses whose progression length is identical to the distance which separates the points of intersection aforementioned. Additionally, if however no progressive ophthalmic lenses corresponded to this distance, the choice of the frame could be reassessed so as to identify an appropriate frame. 
     The direction of gaze of the wearer in a far vision posture corresponds to the direction of gaze when he is standing and observing the horizon. In a near vision posture, the direction of gaze is that of the wearer when he is reading in a natural position, for example a book that he is holding in his hands. 
     According to one particularly advantageous mode of implementation of the invention, said frame is equipped with a calibrated rig exhibiting three tag points spaced apart respectively by a determined distance. As will be explained hereinafter in greater detail, the calibrated rig makes it possible to measure the distance of certain characteristics of the frame in relation to certain other anthropometric characteristics of the wearer. The calculation of certain of these distances by triangulation will also be explained. It will be observed that the calibrated rig makes it possible to avoid putting tags in place on the frame itself. However, it is also possible to use the calibrated rig to measure certain of these distances and also the value of the frame height for example to measure certain other distances. Preferably, the calibrated rig sits in the upper part of the frame and it exhibits two lateral tag points neighboring the arms of the frame and joined by a bridge, as well as a central tag point situated at the end of a rod mounted perpendicularly to the bridge between the two lateral tag points. 
     According to a particularly advantageous characteristic, in the aforementioned step b), a first image of said frame equipped with said calibrated rig and the pupils of the eyes of said wearer is recorded along a direction neighboring said first direction of gaze, so as to determine the position of said first point of intersection with respect to said frame. As will be explained hereinafter, by virtue of the first image and according to an implementation variant, the distance which separates the lower edge of the frame and the corneal reflection of the wearer is measured, as are the relative distances of the aforementioned three tag points so as to determine the angle of the recess mid-plane with respect to a vertical plane. The angle of the mid-plane with respect to the vertical is called the pantoscopic angle. By virtue of these elements, the position of the first point of intersection between the recess mid-plane and the progressive ophthalmic lenses is determined with respect to the lower edge of the frame. 
     Advantageously, a first camera is provided and in that said first camera is adjusted remotely from said wearer fitted with said frame equipped with said calibrated rig and along a direction neighboring said first direction of gaze so as to record said first image. The first camera is for example adjusted to about 2 m from the wearer in a standing position and at the height of his eyes. In this way, the image obtained by the first camera can be processed and analyzed, doing so in an automatic or else semi-automatic manner, so as to obtain the aforementioned values. 
     Furthermore, in step c), a second image of said frame equipped with said calibrated rig and the pupils of the eyes of said wearer is recorded along a direction neighboring said second direction of gaze, so as to determine the position of said second point of intersection with respect to said frame. Measurements and a calculation comparable with that of the aforementioned step b) can be implemented to determine the position of the second point of intersection, for example with respect to the lower edge of the frame. 
     Hence, to do this, a mobile support bearing inscriptions and a second camera secured to said mobile support and installed through said inscriptions are provided, and said wearer fitted with said frame equipped with said calibrated rig is permitted to adjust said mobile support to a natural reading distance, so as to record said second image. Thus, by virtue of the second camera carried on the support bearing the inscriptions, it will be possible to obtain an image of the frame equipped with the rig and the pupil of the wearer&#39;s eyes from the support and along a direction neighboring the second direction of gaze of the wearer. In the same manner, as for the first camera, the image obtained can be processed and analyzed to obtain the position of the second point of intersection with respect to the lower edge of the frame. 
     It will be observed that these measurements and its calculations are simplified when the optical axis of the camera coincides with the direction of gaze of the wearer. If it may be considered that this is the case for the first direction of gaze in the far vision first posture, the same does not hold in the case of the second direction of gaze in the near vision posture. 
     According to another subject, the present invention relates to an automatic processing assembly making it possible to select progressive ophthalmic lenses for a given frame fitted on given wearer, the progressive ophthalmic lenses exhibiting a far vision zone and a near vision zone spaced apart by a progression length, said given frame exhibiting two recesses able respectively to receive a progressive ophthalmic lens, said two recesses defining a recess mid-plane. It comprises: first determination means for determining with respect to said frame, the position of a first point of intersection of a first direction of gaze of said wearer in a far vision posture with said recess mid-plane; second determination means for determining with respect to said frame, the position of a second point of intersection of a second direction of gaze of said wearer in a near vision posture with said recess mid-plane; evaluation means for evaluating the distance which extends between said points of intersection; and, selection means for selecting progressive ophthalmic lenses whose progression length corresponds to said evaluated distance between said points of intersection. 
     Furthermore, said first and second determination means advantageously comprise a calibrated rig intended to equip said frame, and exhibiting three tag points spaced apart respectively by a determined distance. This calibrated rig makes it possible especially, as will be explained in greater detail hereinafter, to determine by triangulation the orientation of the frames but also, the distances at the level of the wearer&#39;s eyes. 
     Moreover, and according to one particularly advantageous mode of implementation of the invention, said second determination means comprise a portable display screen and a camera installed on said portable display screen. The portable display screen for example a “tablet PC”, surmounted by an onboard camera. Thus, and as will be explained hereinafter in greater detail, the wearer can himself adjust the display screen to the natural near vision distance and also, orient the optical axis of the camera. 
     Furthermore, said second determination means advantageously comprise recording and calculation means, for recording the images provided by said camera and for calculating said position of the second point of intersection of the second direction of gaze of said wearer in a near vision posture with said recess mid-plane. 
     Other particular features and advantages of the invention will emerge on reading the description given hereinafter of a particular embodiment of the invention, given by way of nonlimiting indication, with reference to the appended drawings in which: 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic front view of the eyes of a wearer of a frame equipped with a calibrated rig; 
         FIG. 2  is a schematic side view showing the equipped-frame wearer in a far vision posture; 
         FIG. 3  is a schematic detail view of  FIG. 2 ; 
         FIG. 4  is a schematic side view showing the equipped-frame wearer in a near vision posture; 
         FIG. 5  is a schematic detail view of  FIG. 4 ; and, 
         FIG. 6  is a schematic detail view according to another mode of implementation of the invention. 
     
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
       FIG. 1  illustrates  1  illustrates a frame  10  installed on the face  12  of a wearer. This frame  10  exhibits two arms  14 ,  16  and two recesses  18 ,  20  delimited by a substantially ovoid closed structure and which extend respectively in front of the wearer&#39;s eyes  22 ,  24  so as to receive progressive ophthalmic lenses. Furthermore, the frame  10  is equipped with a calibrated rig  26 . This calibrated rig  26  exhibits a bridge  28  which extends longitudinally and two opposite ends  30 ,  32  which respectively comprise a fixing bracket  34 ,  36 . Thus, the fixing brackets  34 ,  36  overlap the frame  10  in the neighborhood of the latter&#39;s two respective arms  14 ,  16 , leaving the wearer&#39;s visual space free. The calibrated rig  26  which is thus totally secured to the frame  10 , exhibits two opposite tags  38 ,  40  installed respectively at the two opposite ends  30 ,  32 . These two opposite tags  38 ,  40  exhibit respectively a white colored mark in the form of a disk, the center of which bears a black point  42 ,  44 . Furthermore, the two black points  42 ,  44  are spaced a known distance apart, for example equal to exactly 110 mm. 
     Moreover, in this figure will be observed the pupils  46 ,  48  of the wearer&#39;s eyes  22 ,  24 , which are able to exhibit at their center a white mark corresponding to the reflection of the vertex of the cornea. Thus, there appears in a front view at one and the same time the calibrated rig  26  and the two black points  42 ,  44  spaced a determined distance apart and in an extremely close neighboring vertical plane, the pupil  46 ,  48  of the wearer&#39;s eyes  22 ,  24 . 
     Furthermore, the frame  10  exhibits a height AC corresponding to the maximum height of the closed structure according to a substantially vertical plane cutting the pupils  46 ,  48 . The points A and C correspond respectively to the upper and lower edges of the frame, and their distance is perfectly determined. 
     In order to implement the method according to the invention, there is also provided a first installation  50  comprising a recording device  52  represented in  FIG. 2 . The recording device comprises at least one digital camera  54  of CCD type oriented toward the face  12  of the wearer at a distance D from the latter, equivalent to 2 m. This first installation also comprises processing means, not represented. They include an image processing module making it possible to evaluate on the basis of the images provided and recorded by the camera  54 , especially the relative position of the lower and upper edges of the frame and of the corneal reflection of the pupils  46 ,  48 . They also include a calculation module making it possible to evaluate the inclination of the mid-plane of the recesses  18 ,  20  with respect to the vertical. Advantageously, a lamp is installed at the level of the camera, so as obtain a very sharp corneal reflection. 
     The wearer is equipped with the frame  10  which is furnished with its calibrated rig  26 . Here, the wearer&#39;s posture corresponds to far vision. 
     In this position, an image of the wearer&#39;s face  12  is recorded with the aid of the digital camera  54 . Attention will now be turned to  FIG. 3  showing the various parameters reproduced in the plane of the image Pl 1 . Thus, the optical axis A 1  of the digital camera  54  substantially cuts the segment which joins the corneal reflection of the two pupils  46 ,  48  and equidistantly from these pupils  46 ,  48 . Hence, the optical axis A 1  of the digital camera  54  is perpendicular to the image plane Pl 1 . Found in this image plane are the upper edge A of the frame  10 , the projection E of the lower edge C, as well as the projection M of the first point of intersection J of the first direction X 1  of gaze of the wearer with the recess mid-plane PL defined by the recesses  18 ,  20  of the frame  10 . It will be observed that the first direction X 1  of gaze of the wearer coincides with the optical axis A 1  of the digital camera  54 . 
     It is desired in this position to ascertain the distance between the first point of intersection J and the lower edge C of the frame. 
     The angle β is firstly determined. The distance TM which separates the digital camera  54  from the projected point M is known. This projected point M is situated equidistantly from the upper and lower edges of the image plane Pl 1 . On the one hand the pixels which separate the point M and the point E and on the other hand the pixels which separate the two black points  42 ,  44  of the calibrated rig  26  are enumerated on the image plane. Knowing the real distance which separates these two black points  42 ,  44 , the real distance ME is deduced therefrom, by applying a rule of three. Thus the angle β is derived from the triangle AEC, since tan (π−β)=TM/ME. 
     Hence, from this is deduced the pantoscopic angle α between the image plane Pl 1  and the recess mid-plane PL since in triangle AEC, α=π−β−arcsin [(AE sin β)/AC]. Taking account of the previous calculation, α=arctan [TM/ME]−arcsin [(AE sin β)/AC]. Furthermore, the length AE is determined as hereinabove, by enumerating the pixels between the point M and the point E of the image plane Pl 1  and by applying a rule of three. 
     The position of the point of intersection J is thus determined by calculating on the one hand the distance AM included in the image plane Pl 1  by enumerating the pixels between the point A and the point M and by applying a rule of three and by dividing this distance by cos α in order to obtain the distance AJ and on the other hand by subtracting the distance AJ from the known distance CA which extends between the two edges, upper and lower, of the frame  10 . The value of the distance CJ is thus obtained. 
     Moreover, still in this far vision posture such as represented in  FIG. 2 , the length which extends between the corneal reflections of the two pupils  46 ,  48  is also measured, by enumerating the pixels which extend between the two reflections projected in the image plane Pl 1  and by applying a rule of three as indicated hereinabove to determine the real distance. 
     The mode of determination of the position of the point of intersection of the direction of gaze of the wearer with the recess mid-plane in a near vision posture will now be described with reference to  FIGS. 4 and 5 . 
     Represented in  FIG. 4  is the wearer equipped with the frame  10  which is furnished with its calibrated rig  26 . According to the method, a second installation  56  is furthermore provided, comprising a second recording device  58  comprising a mobile digital camera  60  of CCD type. This mobile camera  60  is mounted through a support  62  on which inscriptions are featured. Hence, the wearer of the frame  10  is requested to place himself in a natural position for reading the inscriptions of the support. This relative position of the support and of the wearer&#39;s face  12  corresponds to a near vision posture. The optical axis of the camera is then oriented toward the face  12  of the wearer at a calculable distance and along a direction which does not necessarily coincide with the wearer&#39;s direction of gaze. 
     This second installation  56  also comprises processing means, not represented, and they include an image processing module analogous to the previous making it possible to evaluate on the basis of the images provided and recorded by the mobile digital camera  60 , the distance of the latter with respect to the frame  10 , the relative position of the lower and upper edges of the frame and of the corneal reflection of the pupils  46 ,  48 . Just like the previous processing means, they include a calculation module making it possible to evaluate the inclination of the mid-plane of the recesses  18 ,  20  with respect to the vertical. 
     In this near vision posture, an image of the wearer&#39;s face  12  is recorded with the aid of the mobile digital camera  60 . Attention will now be turned to  FIG. 5  showing the various parameters reproduced in the plane of the image Pl 2 . 
     The optical axis A 2  of the mobile digital camera  60  no longer cuts the segment which joins the corneal reflection of the two pupils  46 ,  48  but it extends between this segment and a segment formed by the two upper edges A of the recesses of the frame. 
     On the other hand, the optical axis A 2  of the mobile digital camera  60  is by nature always perpendicular to the image plane Pl 2  which in  FIG. 5  is tangent to the upper edge A of the recesses of the frame. 
     Thus, found in this image plane Pl 2  are the upper edge A of the frame  10 , the projection B of the lower edge C, the intersection M of the optical axis A 2  and of the image plane Pl 2 , as well as the projection I of the second point of intersection O of the second direction X 2  of gaze of the wearer with the second recess mid-plane PL 2  defined by the recesses  18 ,  20  of the frame  10 . 
     It is desired in this position, as in the far vision posture, to ascertain the distance between the second point of intersection O and the lower edge C of the frame. 
     To do this, the distance MV which extends between the mobile digital camera  60  and the point M is firstly determined. This distance is easily determined since it corresponds to a number of pixels between the two black points  42 ,  44  of the calibrated rig  26 . 
     Thereafter, the angle β is determined. The distance MV which separates the mobile digital camera  60  from the point M is therefore known. On the one hand the pixels which separate the point M and the point B and on the other hand the pixels which separate the two black points  42 ,  44  of the calibrated rig  26  are enumerated on the image plane Pl 2 . The real distance MB is deduced therefrom, by applying a rule of three. Thus from this is deduced the angle β of the triangle ABC, since tan β=MV/MB. 
     Hence, from this is deduced the angle α between the image plane Pl 2  and the recess mid-plane PL 2  since in triangle ABC, α=π−β−arcsin [(AB sin β)/AC]. Furthermore, the length Al is determined as hereinabove, by enumerating the pixels between the point M and the point I of the image plane Pl 2  and by applying a rule of three. Moreover, the angle γ=arctan [MV/MI] is calculated so as to obtain the distance AO=Al [sin β/sin (α+γ)]. 
     The distance sought CO is thus determined by subtracting the distance AO from the known distance AC which extends between the two edges, upper and lower, of the frame  10 . 
     It will be observed that the angle α between the image plane Pl 2  and the recess mid-plane PL 2 , can be obtained in a known manner by means of the calibrated rig  26 , by triangulation, by virtue of a third tag situated at the center of the bridge  28  and which extends proud of the bridge. 
     Moreover, still in this near vision posture such as represented in  FIG. 5 , the length which extends between the corneal reflections of the two pupils  46 ,  48  is also measured, by enumerating the pixels which extend between the two reflections projected in the image plane Pl 2  and by applying a rule of three as indicated hereinabove to determine the real distance. 
     Thereafter, the distance which extends between the points of intersection J for the far vision posture and O for the near vision posture is evaluated, by subtracting the value CO obtained by the near vision posture from the value CJ obtained by the far vision posture. 
     Finally, it is then possible to select progressive ophthalmic lenses whose progression length corresponds to said evaluated distance between the points of intersection O and J. 
     According to one particularly advantageous mode of implementation of the invention, illustrated in  FIG. 6 , where the elements and points strictly analogous to the previous illustrated in  FIG. 5  exhibit the same references, while the analogous elements playing the same role are labeled with one and the same reference labeled with a prime sign “′”, the support consists of a portable display screen  62 ′, while the CCD digital camera  60 ′ is installed securely on said portable display screen  62 ′. As will be explained hereinafter, the equipped portable display screen  62 ′, exhibits a two-fold advantage. It makes it possible at one and the same time to orient the optical axis of the camera  60 ′ toward the center of the eye L, thereby making it possible to improve the precision of the measurements, and also to constitute the near vision reading support for the wearer. However, a correction is necessary in order to take account of the position of the camera  60 ′ with respect to the portable display screen  62 ′, and in particular when the optical axis of the camera is inclined with respect to the display screen  62 ′. 
     Thus, with respect to  FIG. 5 , the relative position of the support  62  and now of the display screen  62 ′ is rigorously identical. On the other hand, the digital camera  60 ′ is no longer situated on the optical axis of the eye, but the optical axis of the camera  60 ′ does cut the eye substantially at its center L. Furthermore, the second direction of gaze X 2 ′ is oriented toward a horizontal median  66  of the display screen  62 ′, that it cuts substantially perpendicularly. This horizontal median  66  is here perpendicular to the plane of the figure. 
     Before describing the geometric consequences of this arrangement and determining the main useful parameters thereof, the operative conditions which enable same to be achieved will be explained. 
     Firstly, just as for the support  62  of the previous mode of implementation, the portable display screen  62 ′ is grasped on each side by the wearer, who holds it at his near reading distance. This distance between the center of the eye L and the screen is around 40 cm. Hence, the orientation of the camera  60 ′ with respect to the portable display screen  62 ′ is preadjusted in such a way that the optical axis A 2 ′ of the camera  60 ′ crosses the normal to the screen  62 ′ cutting the center of the aforementioned median, and here coinciding with the second direction of gaze X 2 ′ at about 40 cm from the screen  62 ′. 
     Thereafter, the image obtained by virtue of the camera  60 ′, corresponding to the image plane Pl 2 ′ is retransmitted on the portable display screen  62 ′ in real time. Furthermore, the horizontal median line  66  which separates the screen into two equal parts, top and bottom, is displayed on the portable display screen  62 ′. 
     Thus, the wearer fitted with the frame furnished with the calibrated rig  26  is requested not only to adjust the portable display screen  62 ′ in his normal position of near reading, but also to orient it in such a way that his eyes are centered laterally and that the median line cuts them at the level of the corneal reflection  68 . Once in this position, the image is recorded. Indeed, in this position the optical axis A 2 ′ of the camera  60 ′ cuts the center of the eye L.  FIG. 6  thus schematically illustrates the situation side-on. 
     It will be observed that the optical axis A 2 ′ cuts the recess mid-plane PL 2 ′ at a second point O′, while the second point of intersection of the second direction of gaze X 2 ′ cuts the recess mid-plane PL 2 ′ at a point K. 
     Here it is quite obviously the value of the distance CK that should be sought. 
     The value of the distance AO′ is firstly easily determined since the angle α between the image plane Pl 2 ′ and the recess mid-plane PL 2 ′ in the triangle ABC is already known and the distance AM′ in the image plane Pl 2 ′ is determined by calculating the number of pixels and applying a rule of three. The optical axis A 2 ′ cutting by definition the image plane Pl 2 ′ in a perpendicular manner, the distance AO′ is therefore equivalent to AM/cos α. 
     It is now appropriate to determine the distance which separates the point O′ from the point K. 
     Firstly, the distance which separates the point V′ of the camera  60 ′ at the point O′ of the recess plane PL 2 ′ is ascertained by evaluating the number of pixels on the calibrated rig  26  and by operating a rule of three. Moreover, the distance which separates along this direction of the optical axis A 2 ′, the recess plane PL 2 ′ from the cornea of the eye at the level of the corneal reflection  68  has already been calculated, and it equals about 1.3 cm. And the mean radius R of an eye is known, about 0.8 cm, i.e. also the total distance LO′. Hence, the distance from the center of the eye L to the optical center V′ of the camera  60 ′ is deduced therefrom quite naturally. Moreover the distance h which separates the camera  60 ′ from the horizontal median line  66  is known. Consequently, the center of the eye L, the optical center of the camera  60 ′ and the point of intersection of the second direction of gaze X 2 ′ with the median line  66  forming a right-angled triangle, the value of the angle θ between the second direction of gaze X 2 ′ and the optical axis A 2 ′, and more precisely sin θ, is known and equals h/LV′. 
     Now, at the level of the triangle L, O′, K, recognizes the distance LO′, and the sin θ of the angle between the segments LK and LO′. We must then determine the angle Ω between the segments LO′ and O′K in order to be able to evaluate the segment O′K. 
     The angle Ω, is equivalent to the difference between π and the angle δ between the segment O′A and the segment O′M′. Now, the angle δ equals π/2−α, and consequently the angle Ω equals α+π/2. 
     Hence, knowing the length of a side of a triangle common to its two of its angles, from this is deduced the length of another side. And in this instance, O′K is equal to the ratio of the product O′L·sin θ and of sin (θ+α+π/2). All these values being known, the value O′K is deduced therefrom quite naturally, and so the value of the segment AK, and more interestingly the value of CK, between the lower edge B of the frame and the center of the near vision K on the frame. 
     It will be observed that the calculation of the distance O′K is substantially different when the camera  62 ′ is oriented in such a way that its optical axis A 2 ′ is perpendicular to the portable display screen  62 ′, since in this case, the camera is parallel to the image plane Pl 2 ′. Hence it is no longer the sine of the angle θ which is determined but its tangent h/V′L.