Patent Publication Number: US-2020285058-A1

Title: Optical device, retinal projection display, head-mounted display, and optometric apparatus

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This patent application is based on and claims priority pursuant to 35 U.S.C. § 119(a) to Japanese Patent Application No. 2019-040841, filed on Mar. 6, 2019, Japanese Patent Application No. 2019-120426, filed on Jun. 27, 2019, and Japanese Patent Application No. 2020-028225, filed on Feb. 21, 2020 in the Japan Patent Office, the entire disclosure of which is incorporated by reference herein. 
     BACKGROUND 
     Technical Field 
     The present disclosure relates to an optical device, a retinal projection display, a head-mounted display, and an optometric apparatus. 
     Description of the Related Art 
     A technology for detecting a pupil position (line of sight) has been developed, and application of the technology to various purposes of use is expected. Examples of the purposes of use include an interface for control on an electronic apparatus, assistance for forming an image by a wearable display such as a head-mounted display, data collection on lines of sight of, for example, skilled technicians, and attention analysis for products. A pupil-position detecting device is demanded for responsivity of detection and decreases in size and weight of a detecting device. 
     SUMMARY 
     An optical device according to an embodiment includes a light source section configured to emit light; a converging reflector configured to converge and reflect the light from the light source section to an irradiation surface having a curvature; and a position detector configured to detect a position of the light reflected from the irradiation surface. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The aforementioned and other aspects, features, and advantages of the present disclosure would be better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein: 
         FIG. 1  illustrates an example arrangement of a pupil-position detecting device according to a first embodiment; 
         FIGS. 2A and 2B  illustrate a relationship between a rotation of an eyeball and an incident position of a laser beam on a position sensitive detector (PSD),  FIG. 2A  illustrating a state where the eyeball does not rotate,  FIG. 2B  illustrating a state where the eyeball rotates; 
         FIGS. 3A and 3B  illustrate conditions to be satisfied by an off-axis optical system,  FIG. 3A  illustrating distances among elements,  FIG. 3B  illustrating a geometrical distance relationship expressed using a coaxial optical system; 
         FIG. 4  illustrates an example of a relationship between the diameter of an effective region of a concave mirror and the radius of a laser beam on a light receiving surface of the PSD; 
         FIG. 5  is a block diagram illustrating an example of a hardware configuration of a processor according to the first embodiment; 
         FIG. 6  is a block diagram illustrating an example of a functional configuration of the processor according to the first embodiment; 
         FIG. 7  is a flowchart of an example of processing by a pupil-position detecting device according to the first embodiment; 
         FIGS. 8A and 8B  each (first illustration) illustrate an example arrangement of a major part of a pupil-position detecting device according to a first modification,  FIG. 8A  illustrating an arrangement in which an optical path from a vertical cavity surface emitting laser (VCSEL) to a concave mirror intersects with an optical path from an eyeball to a PSD,  FIG. 8B  illustrating an arrangement in which an optical path from a VCSEL to a concave mirror does not intersect with an optical path from an eyeball to a PSD; 
         FIG. 9  (second illustration) illustrates an example arrangement of a major part of a pupil-position detecting device according to a second modification; 
         FIG. 10  (third illustration) illustrates an example arrangement of a major part of a pupil-position detecting device according to a third modification; 
         FIGS. 11A-a  and  11 A-b (fourth-a illustration) each illustrates an example arrangement of a major part of a pupil-position detecting device according to a fourth-a modification,  FIG. 11A-a  being a view from above the major part and  FIG. 11A-b  being a view from the eyeball side of part B of  FIG. 11A-a ; 
         FIGS. 11B-a ,  11 B-b, and  11 B-c (fourth-b illustration) each illustrates an example arrangement of a major part of a pupil-position detecting device according to a fourth-b modification,  FIG. 11B-a  being a view from above the major part,  FIG. 11B-b  being a view from the eyeball side of part B in  FIG. 11B-a , and  FIG. 11B-c  being a view of part B in FIG.  11 B-a from the opposite side of the eyeball; 
         FIG. 12  (fifth illustration) illustrates an example arrangement of a major part of a pupil-position detecting device according to a fifth modification; 
         FIGS. 13A and 13B  each (sixth illustration) illustrate an example arrangement of a major part of a pupil-position detecting device according to a sixth modification,  FIG. 13A  being a view of a concave mirror from a side facing a concave surface,  FIG. 13B  being a cross-sectional view taken along line A-A′ in  FIG. 13A ; 
         FIGS. 14A and 14B  each (seventh illustration) illustrate an example arrangement of a major part of a pupil-position detecting device according to a seventh modification,  FIG. 14A  being a view from above the major part,  FIG. 14B  being a view from the eyeball side of part C of  FIG. 14A ; 
         FIG. 15  illustrates an example arrangement of a non-coaxial concave mirror; 
         FIG. 16  illustrates an example of a non-diffracted beam; 
         FIGS. 17A-a  and  17 A-b illustrate an example arrangement of an off-axis optical system using a holographic optical device (HOE),  FIG. 17A-a  illustrating a case where a HOE generates one convergent laser beam,  FIG. 17A-b  illustrating a case where a HOE generates a plurality of convergent laser beams; 
         FIG. 17B  illustrates a converging reflector including a liquid-crystal reflective condenser structure; 
         FIG. 17C  illustrates an orientation state of liquid crystal molecules in the liquid-crystal reflective condenser structure; 
         FIGS. 17D-a  and  17 D-b each illustrate a polarized state of incident and outgoing rays by the liquid-crystal reflective condenser structure; 
         FIG. 17E  illustrates a light-guide coupling optical system using the liquid-crystal reflective condenser structure; and 
         FIG. 18  illustrates an example arrangement of a retinal projection display according to a second embodiment. 
     
    
    
     The accompanying drawings are intended to depict embodiments of the present disclosure and should not be interpreted to limit the scope thereof. The accompanying drawings are not to be considered as drawn to scale unless explicitly noted. 
     DETAILED DESCRIPTION OF EMBODIMENTS 
     In describing embodiments illustrated in the drawings, specific terminology is employed for the sake of clarity. However, the disclosure of this patent specification is not intended to be limited to the specific terminology so selected and it is to be understood that each specific element includes all technical equivalents that operate in a similar manner and achieve similar results. 
     Although the embodiments are described with technical limitations with reference to the attached drawings, such description is not intended to limit the scope of the disclosure and all of the components or elements described in the embodiments of this disclosure are not necessarily indispensable. 
     Referring now to the drawings, embodiments of the present disclosure are described below. In the drawings for explaining the following embodiments, the same reference codes are allocated to elements (members or components) having the same function or shape and redundant descriptions thereof are omitted below. 
     Embodiments of the present disclosure are described referring to the drawings. Like reference signs are applied to identical or corresponding components throughout the drawings and redundant description thereof may be omitted. 
     A pupil-position detecting device for an eyeball is described as an example of an optical device, and a case where the pupil-position detecting device is mounted on an eyeglass-shaped support is described as an example according to embodiments. 
     In each embodiment, the right eyeball of a “person” is described for example; however, each embodiment may be applied to the left eyeball likewise. Alternatively, two optical devices or two retinal projection displays may be provided and applied to eyeballs of both eyes. 
       FIG. 1  illustrates an example arrangement of a pupil-position detecting device  10  according to a first embodiment. 
     As illustrated in  FIG. 1 , the pupil-position detecting device  10  includes a vertical cavity surface emitting laser (VCSEL)  1 , a concave mirror  2 , a position sensitive detector (PSD)  3 , and a processor  100 . 
     The VCSEL  1 , the concave mirror  2 , and the PSD  3  are disposed on an optical-system support  4 . The optical-system support  4  is secured to an eyeglass frame  22  of an eyeglass-shaped support  20  so that the optical-system support  4  can be inclined via a ball joint  4   a.  The eyeglass-shaped support  20  includes eyeglass lenses  21  and the eyeglass frame  22 . Since the optical-system support  4  is secured via the ball joint  4   a,  the inclination of the optical-system support  4  can be adjusted. The ball joint  4   a  constituting an installation fine adjustment mechanism is fixed by, for example, using magnetic force acting between the magnetized spherical structure and metal opening structure, in addition to applying a mechanical pressure between the spherical structure and the outer shell structure. 
     The eyeglass-shaped support  20  can be mounted on the head of a person. When the eyeglass-shaped support  20  is mounted, an optical system including the VCSEL  1 , the concave mirror  2 , and the PSD  3  is arranged at a position near an eyeball  30  (in front of the eye). 
     The VCSEL  1  which is an example of a “light source section” includes a plurality of light emitting portions two-dimensionally arrayed in a plane. Each light emitting portion emits a laser beam having a directivity and a limited angle of divergence. The emitted laser beam is an example of “light”. The “plurality of light emitting portions” are equivalent to “a plurality of light emitting spots” or “a plurality of light emitting elements”. 
     The light source section is not limited to the VCSEL as far as the light source section can emit light. Alternatively, a plurality of semiconductor laser diodes (LDs) or a plurality of light emitting diodes (LEDs) that emit laser beams may be two-dimensionally arrayed in a plane to constitute a light source section. Still alternatively, a pulsed laser that emits a pulsed laser beam may be used. Yet alternatively, a plurality of types of light sources may be combined to constitute a light source section. 
     The laser beams emitted from the VCSEL  1  desirably have a wavelength of near infrared light which is invisible light not to interrupt visual recognition by a “person” whose pupil position is to be detected. However, the wavelength of the laser beams is not limited to the wavelength of invisible light, and may be a wavelength of visible light. 
     A laser beam Lo emitted from the VCSEL  1  propagates toward the concave mirror  2  in a space in front of the eye, in a direction substantially parallel to the facial surface of the person who wears the eyeglass-shaped support  20  or the lens surface of the worn eyeglass lens  21 . The laser beam Lo is divergent light that propagates while the diameter of the beam is increased by diffraction at an opening of an emission part of the VCSEL  1 . The angle of divergence of the divergent light can be controlled in accordance with the shape of the opening of the emission part. The laser beam Lo propagates while diverging and is incident on the concave mirror  2 . 
     The concave mirror  2  serving as an example of a converging reflector has a reflecting surface having a curvature. The concave mirror  2  reflects the incident laser beam L 0  to emit a convergent laser beam (also referred to as convergent light) L 1  on the eyeball  30 . The convergent laser beam L 1  is incident on a portion near a pupil  31  of the eyeball  30 . The center of curvature of the concave surface of the concave mirror  2  is located at a position deviated from the optical axis of an optical path from the VCSEL  1  to the concave mirror  2 . The optical system including the VCSEL  1 , the concave mirror  2 , and the PSD  3  constitutes a so-called off-axis optical system. 
     In the off-axis optical system according to the embodiment, light before reaching the eyeball  30  propagates in a space located in front of the eye and being adjacent to the eyeball  30  while being folded back at least one time without being reflected or scattered by the eyeball  30 , and then reaches the eyeball  30 . 
     The incident angle of the convergent laser beam L 1  on the eyeball  30  is adjusted so that the convergent laser beam L 1  is incident on the center of the pupil  31  of the eyeball  30  at a predetermined angle in normal vision. The VCSEL  1  can emit laser beams from the plurality of light emitting portions. The laser beams emitted from the plurality of light emitting portions are emitted on a plurality of portions of the eyeball  30 , or emitted on the eyeball  30  at a plurality of angles. 
     The VCSEL  1 , which includes a plurality of light emitting portion, provides high-speed modulation. The laser beam emitted on the eyeball is time-modulated, and a component having a modulation frequency adopted for the incident laser beam is extracted from a signal output from the PSD. Thus, the influence of light from the external environment (without modulation) is eliminated. As a result, the SN ratio can be improved, which is advantageous in detecting the pupil position in a bright environment. Further, the amount of laser light to be emitted on the eyeball can be reduced. 
     The pupil surface (cornea surface) of the eyeball  30  serving as an example of a irradiation surface is a transparent body containing moisture, and typically has a reflectivity of about 2% to 4%. The convergent laser beam L 1  incident on a portion near the pupil  31  of the eyeball  30  is reflected by the surface of the pupil  31  of the eyeball  30  (also referred to as reflected light), and the reflected light propagates toward the PSD  3 . In the following description, to simplify the description, the surface of the eyeball  30  may be referred to as eyeball  30 , the surface of the pupil  31  may be referred to as pupil  31 , and the surface of a cornea  32  may be referred to as cornea  32 . 
     In this case, the curvature of the reflecting surface of the concave mirror  2  is determined to cancel out the divergence of the reflected laser beam based on the curvature of the eyeball  30  or the cornea  32 . Thus, the diameter of a laser beam L 2  propagating toward the PSD  3  does not expand on the light receiving surface of a PSD element. 
     The concave mirror is described as an example of the converging reflector; however, the example is not limited thereto as far as the element can converge (condense) light. A configuration having a combination of a convex lens and a plane mirror, a wavefront control element using a hologram, or a diffraction optical element may be used. 
     The concave surface of the concave mirror may use an anamorphic aspherical surface having different curvatures in orthogonal two directions in a plane which intersects with the optical axis of the convergent laser beam L 1 . Using the anamorphic aspherical surface can further decrease the diameter of the laser beam L 2  and isotropically shape the beam. 
     Furthermore, the irradiation surface is not limited to the eyeball  30 , and the embodiment may be applied to any three-dimensional object having a curvature. 
     The PSD  3  serving as an example of a “position detector” is a two-dimensional light-position detecting element that detects current values of incident light in accordance with the distances to an electrode in two directions orthogonal to each other within the light receiving surface, and calculates and outputs a detection signal indicating the position of the incident light based on the current values in the orthogonal two directions. The PSD  3  can output a detection signal indicating the position of a beam spot formed on the light receiving surface of the PSD  3 . 
     More specifically, the PSD  3  includes four output terminals. A resistance film is disposed on a continuous light receiving surface (a light receiving surface having pixels that are not divided). The PSD  3  includes a pair of electrodes in the orthogonal two directions. Photocurrent generated at a beam spot position is divided into four in accordance with the distances to the respective output terminals. At this time, an electrical resistance due to the resistance film acts so that current decreases as the distance between the beam spot position and the output terminal increases. The PSD  3  can detect electrical signals passing through the resistance film via four terminals, and output a detection signal indicating the position within the light receiving surface obtained through electrical post processing. 
     The PSD  3  can convert current generated by photoelectric conversion into analog voltage signals, and output the analog voltage signals as detection signals from the four terminals. That is, the PSD  3  obtains the distances from the respective terminals using the surface resistances to detect the incident position. 
     Instead of the PSD  3 , if an image sensor (imaging element) is applied to the position detector, the output result of the image sensor changes in accordance with the intensity of incident light on each pixel, and the output current decreases as the intensity decreases. To reduce the influence of noise light such as sunlight, the output of the light source is required to be increased to increase the intensity of incident light on the image sensor. However, when the embodiment is applied to a device that causes light from a light source to be incident on the eyeball  30 , increasing the intensity of incident light is not desirable in the viewpoint of safety of the eyeball. 
     In the case of the image sensor, image processing for position detection is required. A positional accuracy may have an error during processing, and a processing burden may increase. 
     Since the PSD  3  is used for the position detector, the position is detected by using a current division ratio (proportion) of division among the output terminals. This is advantageous because the position of incident light can be detected irrespective of the intensity of incident light, and image processing is not required. 
     The configuration of the above-described PSD  3  is an example, and another configuration may be employed. The example of the two-dimensional PSD that detects a two-dimensional position within the light receiving surface is provided for the PSD  3 . Alternatively, a one-dimensional PSD that detects a one-dimensional position within the light receiving surface may be used. 
     The processor  100  outputs a control signal to drive the VCSEL  1  for light emission. The processor  100  also receives the detection signal from the PSD  3  to execute processing of detecting the position of the pupil  31  of the eyeball  30 , which will be described later. The processor  100  can be disposed on, for example, the eyeglass frame  22 . 
     The laser beam L 2  forms a beam spot on the light receiving surface of the PSD  3 . The position of the beam spot is changed in accordance with the inclination of the eyeball  30 . The processor  100  converts the detection signal of the PSD  3  into coordinate information to detect the pupil position of the eyeball  30 . 
     The PSD  3  can detect the direction of a normal vector and the position of a reflection point on the eyeball  30 . The pupil-position detecting device  10  can “estimate” the pupil position based on the correspondence between the detected position of the reflection point and the detected normal vector of the reflection point and the detected surface shape model of an eyeball. 
       FIG. 1  illustrates the example in which the optical system and the processor are disposed on the eyeglass frame  22 . However, the arrangement is not limited thereto. A head-mounted display or a headgear-shaped holding structure may be used. 
     A tracking operation of the pupil-position detecting device  10  to an eyeball movement is described next. 
     The eyeball  30  makes an eyeball movement such as a rotation. When the eyeball  30  rotates and the direction of the laser beam L 2  is changed by the rotation, the laser beam L 2  may be deviated from the light receiving surface of the PSD  3 . In contrast, the pupil-position detecting device  10  performs control to sequentially or selectively change the light emitting portion for light emission of the VCSEL  1 . Thus, the laser beam L 2  can be prevented from being deviated from the light receiving surface of the PSD  3 . 
       FIGS. 2A and 2B  illustrate a relationship between a rotation of the eyeball  30  and an incident position of the laser beam L 2  on the PSD  3 ,  FIG. 2A  illustrating a state where the eyeball does not rotate (in normal vision),  FIG. 2B  illustrating a state where the eyeball rotates. 
       FIGS. 2A and 2B  illustrate propagation of laser beams emitted from two light emitting portions of the VCSEL  1 . A laser beam  11  emitted from one of the light emitting portions is indicated by solid lines. A laser beam  12  emitted from the other one of the light emitting portions is indicated by broken lines. 
     Referring to in  FIG. 2A , the laser beam  11  reflected by the eyeball  30  is incident on a portion near the center of the light receiving surface of the PSD  3 . The PSD  3  can detect the position of the laser beam  11  on the light receiving surface of the PSD  3 . The pupil-position detecting device  10  can detect the position of the pupil  31  based on the detection signal of the PSD  3 . 
     In contrast, the laser beam  12  reflected by the eyeball  30  is not incident on the light receiving surface of the PSD  3 . Thus, the PSD  3  does not detect the position of the laser beam  12  on the light receiving surface of the PSD  3 . The pupil-position detecting device  10  does not detect the position of the pupil  31 . 
     When the eyeball  30  largely rotates, as illustrated in  FIG. 2B , the laser beam  11  reflected by the eyeball  30  is not incident on the light receiving surface of the PSD  3 . The PSD  3  does not detect the position of the laser beam  11  on the light receiving surface of the PSD  3 . The pupil-position detecting device  10  does not detect the position of the pupil  31 . 
     In contrast, the laser beam  12  reflected by the eyeball  30  is incident on a portion near the center of the light receiving surface of the PSD  3 . Thus, the PSD  3  can detect the position of the laser beam  12  on the light receiving surface of the PSD  3 . The pupil-position detecting device  10  can detect the position of the pupil  31  based on the detection signal of the PSD  3 . 
     In this way, with the light from one light emitting portion, the pupil position of the eyeball  30  can be detected within a limited angular range. However, by changing the light emitting portion of the VCSEL  1 , the laser beam emitted from at least one of the light emitting portions can be incident on the light receiving surface of the PSD  3 . Thus, the frequency of occurrence of a phenomenon in which the laser beam reflected by the eyeball  30  is not incident on the light receiving surface of the PSD  3  is reduced even when the eyeball  30  is rotated, and the detectable range for the pupil position can be expanded. 
     In other words, the PSD  3  detects a fine motion of the laser beam  12  based on the rotation movement of the eyeball  30 , and the array of the plurality of light emitting portions of the VCSEL  1  detects a rough motion of the laser beam  12  based on the rotation movement of the eyeball  30 . Thus, when the rotation angle of the rotation movement of the eyeball  30  is detected, high detection resolution and wide detection range can be obtained. 
     The light emitting portion of the VCSEL  1  can be changed chronologically based on the drive signal from the processor  100  in accordance with (by tracking) the eyeball movement of the eyeball  30 . Since the light emitting portion is controlled in accordance with the rotation movement of the eyeball  30 , light utilization efficiency can be increased and the time required for estimation can be decreased. 
     However, the light emitting portion of the VCSEL  1  does not have to be changed in accordance with the rotation movement of the eyeball. For example, the pupil-position detecting device  10  may cause the light emitting portions of the VCSEL  1  to perform raster scanning (sequential emission) at an interval of a predetermined period independently from the eyeball movement, and detect a rough movement position of the eyeball  30  based on the detection signal of the PSD  3  in this case. 
     To simplify the description,  FIGS. 2A and 2B  illustrate laser beams emitted from the two light emitting portions; however, the VCSEL  1  can use more light emitting portions in accordance with the rotation of the eyeball  30 . In this case, it is desirable to optimize the number and positions of the light emitting portions of the VCSEL  1  to meet the size of the light receiving surface of the PSD  3  and the size of the eyeball  30  so that the position of the pupil  31  is properly detected. 
     Conditions to be satisfied by the off-axis optical system including the VCSEL  1 , the concave mirror  2 , and the PSD  3  are described next. 
     In the embodiment, a diameter of an effective region (a region capable of reflecting a laser beam, or an effective diameter) of the concave mirror  2  is determined for a condition under which a laser beam emitted from the VCSEL  1  is incident on the light receiving surface of the PSD  3 , and a condition under which the convergent laser beam L 1  is converted into parallel light after being reflected by the cornea  32 . 
       FIGS. 3A and 3B  illustrate conditions to be satisfied by the off-axis optical system.  FIG. 3A  illustrates distances among elements.  FIG. 3B  illustrates a geometrical distance relationship expressed using a coaxial optical system. 
     As illustrated in  FIG. 3A , it is assumed that do is a distance from the VCSEL  1  to the concave mirror  2 , d 1  is a distance from the concave mirror  2  to the cornea  32 , and d 2  is a distance from the cornea  32  to the PSD  3 . Focusing on the curvature and the effective region of the concave mirror  2 , a coaxial optical system in which the VCSEL  1 , the concave mirror  2 , and the PSD  3  are coaxially arranged is expected for easier understanding. 
       FIG. 3B  illustrates a state in which a divergent laser beam from the VCSEL  1  is incident on the concave mirror  2 , a laser beam reflected by the concave mirror  2  is incident on the cornea  32  while the laser beam converges and then a laser beam reflected by the cornea  32  is incident on the PSD  3 . A position  41  indicates a position of a light emitting portion of the VCSEL  1 . A position  42  indicates a position on the surface of the cornea  32 . A position  43  indicates a position on the surface of the concave mirror  2 . 
     A radius h PSD  of a beam can be calculated using the following Expression (1) derived by ray tracing using an ABCD matrix. 
     
       
         
           
             
               
                 
                   
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     Based on Expression (1), the diameter D m  of the effective region of the concave mirror  2  can be determined using Expression (2). 
     
       
         
           
             
               
                 
                   
                     
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       FIG. 4  illustrates an example of a relationship between the diameter D m  of the effective region of the concave mirror  2  obtained based on Expression (2) and the radius h PSD  of the laser beam on the light receiving surface of the PSD  3 . 
     In the relationship illustrated in  FIG. 4 , the upper limit value of the radius h PSD  of the laser beam on the light receiving surface of the PSD  3  is h UL  of 200 μm, the distance d 1  from the concave mirror  2  to the cornea  32  is 24 mm, the curvature radius r c  of the cornea  32  is 8 mm, and the wavelength λ of the laser beam is 940 nm. The values are expected values for the eyeglass-shaped support  20 ; however, desirable values may be set in accordance with the purpose of use and environment of use. 
     Referring to  FIG. 4 , when the diameter D m  of the effective region of the concave mirror  2  decreases, the radius h PSD  of the beam on the light receiving surface PSD  3  rapidly increases due to diffraction. When the diameter D m  of the effective region of the concave mirror  2  increases, the radius h PSD  of the beam on the light receiving surface PSD  3  gradually increases. As the radius h PSD  of the beam increases, the position detection resolution of the laser beam by the PSD  3  decreases. 
     As illustrated in  FIG. 4 , to minimize the radius h PSD  of the beam on the light receiving surface of the PSD  3 , there is a proper range for the diameter D m  of the effective region of the concave mirror  2 . A region with gray hatching is a proper range that is a range for the diameter D m  of the effective region of the concave mirror  2  that satisfies Expression (2). Using Expression (2), the diameter D m  of the effective region of the concave mirror  2  is determined by 0.225 mm≤D m ≤2.574 mm. If the condition is satisfied, the radius h PSD  of the beam on the light receiving surface of the PSD  3  can be 200 μm or less, properly setting the position detection resolution for the laser beam by the PSD  3 . 
     When a condition of d 0 =24√3 (mm) is set for a condition under which a laser beam is incident on the eyeball  30  at an incident angle of 60°, the laser beam emitted from the VCSEL  1  requires an angle of divergence of about 7.1° or less for the entire angle. The angle of divergence can be provided through control on the opening of the VCSEL  1 . 
     A hardware configuration of the processor  100  according to the embodiment is described next.  FIG. 5  is a block diagram illustrating an example of the hardware configuration of the processor  100 . 
     The processor  100  includes a central processing unit (CPU)  101 , a read only memory (ROM)  102 , a random access memory (RAM)  103 , a solid state drive (SSD)  104 , a light-source drive circuit  105 , an analog/digital (A/D) conversion circuit  106 , and an input/output interface (I/F)  107 . The components of the processor  100  are coupled to one another by a system bus  108 . 
     The CPU  101  loads into the RAM  103  a program and data from a storage device, such as the ROM  102  or the SSD  104 , and executes processing to provide the control or functions (described later) of the entirety of the processor  100 . A part or the entirety of the functions of the CPU  101  may be implemented by hardware, such as an application specific integrated circuit (ASIC) or a field-programmable gate array (FPGA). 
     The ROM  102  is a non-volatile semiconductor memory (storage device) that holds a program and data although the power is turned off. The ROM  102  stores programs and data of, for example, a basic input/output system (BIOS) and an operating system (OS) that are executed when the processor  100  is activated. The RAM  103  is a volatile semiconductor memory (storage device) that temporarily holds a program and data. 
     The SSD  104  is a non-volatile memory that stores a program that executes processing by the processor  100  and various data. The SSD may be alternatively a hard disk drive (HDD). 
     The light-source drive circuit  105  is an electric circuit that is electrically coupled to the VCSEL  1  and that outputs a drive signal such as a drive voltage to the VCSEL  1  in accordance with a received control signal. The light-source drive circuit  105  can simultaneously or sequentially drive the plurality of light emitting portions included in the VCSEL  1  for light emission. Moreover, the light-source drive circuit  105  modulates the period of the drive voltage, and hence can drive the light emitting portions with different periods of light emission. 
     The drive voltage may use a rectangular wave, a sine wave, or a voltage waveform having a predetermined waveform. The light-source drive circuit  105  can change the period (frequency) of the voltage waveform to modulate the period of the drive voltage signal. 
     The A/D conversion circuit  106  is an electric circuit that is electrically coupled to the PSD  3 , that converts an analog voltage signal output from the PSD  3  into a digital voltage signal, and that outputs the digital voltage signal. 
     The input/output I/F  107  is an interface for connection with an external apparatus, such as a personal computer (PC) or an image apparatus. 
     A functional configuration of the processor  100  according to the embodiment is described next.  FIG. 6  is a block diagram illustrating an example of the functional configuration of the processor  100 . As illustrated in  FIG. 6 , the processor  100  includes a light-emission drive unit  110 , a detection-signal input unit  111 , an arithmetic unit  120  as an example of a calculator, and a pupil-position output unit  130 . 
     The light-emission drive unit  110  outputs a drive signal with a period T 1  to the VCSEL  1  to drive a light emitting portion included in the VCSEL  1  with the period T 1  for light emission. The light-emission drive unit  110  can be implemented by a light-source drive circuit  105  or the like. 
     The detection-signal input unit  111  is implemented by the A/D conversion circuit  106  or the like. The detection-signal input unit  111  converts an analog voltage signal input from the PSD  3  into a digital voltage signal and outputs the digital voltage signal to an eyeball-rotation-angle estimation unit  121  included in the arithmetic unit  120 . 
     The arithmetic unit  120  includes the eyeball-rotation-angle estimation unit  121  and a pupil-position acquisition unit  122 . The arithmetic unit  120  executes arithmetic processing of acquiring the pupil position of the eyeball  30  based on an input signal from the detection-signal input unit  111 . 
     The eyeball-rotation-angle estimation unit  121  estimates the rotation angle of the eyeball  30  based on the input signal from the detection-signal input unit  111 , and outputs an estimated rotation angle data to the pupil-position acquisition unit  122 . The pupil-position acquisition unit  122  executes processing of acquiring the position of the pupil  31  based on the estimated rotation angle of the eyeball  30 . Acquired positional data of the pupil  31  is output to an external apparatus or the like via the pupil-position output unit  130  that is implemented by the input/output I/F  107  or the like. 
     Processing by the pupil-position detecting device according to the embodiment is described next. 
     For preparation to detect the pupil position, the pupil-position detecting device  10  previously determines expressions for the incident angle at which a laser beam emitted by the VCSEL  1  to the eyeball  30  is incident on the eyeball  30  and for the rotation angle of the eyeball  30 . Hence, the expressions are described first. 
     The expression for the rotation angle of the eyeball  30  is an expression of a linear function or a quadratic function. However, the expression is not limited thereto, and may be any expression as far as the expression can determine the incident angle of a laser beam and the rotation angle from the position on the light receiving surface of the PSD  3 . For a simple approximate expression, the embodiment employs an expression of a quadratic function. 
     To determine the angle at which a laser beam is incident on the eyeball  30 , a surface shape model of the eyeball  30  can be used. For example, a reduced schematic eye (for example, see “Optical Mechanism of An Eye”, Journal of the Japan Society of Precision Engineering 27-11, 1961) which has been well known as a surface profile model of a typical eyeball can be used. 
     The incident angle of a laser beam on the eyeball  30  is previously determined through a ray tracing calculation or the like in such a way that the incident position of the laser beam on the PSD  3  is located at the center of the light receiving surface. 
     The incident position of the laser beam on the light receiving surface of the PSD  3  can be theoretically analyzed based on the incident angle of a laser beam on the eyeball  30 , the reflected position of the laser beam at the eyeball  30 , and the inclination of a tangent plane of the eyeball  30 . The solution of the theoretical analysis can determine an inverse operational expression (approximate expression) for estimating the rotation angle of the eyeball  30  through approximation using a polynominal expression. 
     The incident angle of the laser beam on the eyeball  30  and the inverse operational expression for estimating the rotation angle of the eyeball  30  are stored in a memory, such as the ROM  102  or the SSD  104  of the processor  100 ; and are referred when the light-emission drive unit  110  changes the light emitting portion and when the arithmetic unit  120  executes pupil-position acquisition processing. 
       FIG. 7  is a flowchart of an example processing by the pupil-position detecting device according to the embodiment. 
     In step S 71 , the light-emission drive unit  110  drives the VCSEL  1  with the period T 1  for light emission. 
     In step S 72 , the detection-signal input unit  111  receives a detection signal of the PSD  3  and outputs the detection signal to the eyeball-rotation-angle estimation unit  121  included in the arithmetic unit  120 . 
     In step S 73 , the eyeball-rotation-angle estimation unit  121  substitutes the input signal from the detection-signal input unit  111  into the inverse operational expression for estimating the eyeball rotation angle. The calculated eyeball-rotation-angle data is output to the pupil-position acquisition unit  122 . 
     In step S 74 , the pupil-position acquisition unit  122  acquires pupil-position data based on the input eyeball-rotation-angle data using the surface profile model of an eyeball. The acquired pupil-position data is output to an external apparatus via the pupil-position output unit  130 . 
     In this way, the processor  100  can acquire the position of the pupil  31  of the eyeball  30  based on the detection signal output from the PSD  3 , and output the acquired positional data to the external apparatus. 
     A technology for detecting a pupil position (line of sight) has been developed, and application of the technology to various purposes of use is expected. Examples of the purposes of use include an interface for control on an electronic apparatus using a line of sight, assistance for forming an image by a wearable image display such as a head-mounted display or a front-of-eye (near-eye) display, data collection on lines of sight of, for example, skilled technicians in factories, and attention analysis for products (logging). In particular, a pupil-position detecting device that functions as an interface between an electronic apparatus and a person is demanded for real-time response and decreases in size and weight of the detecting device. 
     In related art, a reflected image from an eyeball is acquired under an illumination environment to detect a pupil position using an image processor based on pattern matching. The image processing has a large burden and has a relationship of trade-off between real-time response and detection resolution of the pupil position. Moreover, an imaging device, a processor, a drive power source, and so forth, have to be mounted, resulting in a difficulty in decreases in size and weight. 
     In addition, in related art, a technology that detects a change in time of the intensity of reflected light of a laser beam, which has scanned the surface of an eyeball at a high speed; and that detects a pupil position at a high speed according to a non-image method not using an imaging system is disclosed. With the technology, however, the diameter of the laser beam is expanded on the light receiving surface of a photodetector due to reflection at the eyeball or cornea having a large curvature. Thus, the pupil position may not be properly detected. 
     According to the embodiment, the off-axis optical system is arranged in front of an eye, the off-axis optical system including the VCSEL  1  that emits light, the concave mirror  2  that converts the light into convergent light and folds back the convergent light toward an irradiation surface having a curvature, and the PSD  3  that receives reflected light of the convergent light by the irradiation surface and detects the position of the reflected light. 
     More specifically, the light before reaching the eyeball  30  propagates in a space located in front of the eye and being adjacent to the eyeball  30  while being folded back at least one time without being reflected or scattered by the eyeball  30 , and then reaches the eyeball  30 . The concave mirror  2  irradiates the eyeball  30  with a convergent laser beam. 
     The curvature of the convergent laser beam can cancel out the curvature of the eyeball  30  or the cornea  32 . Thus, the laser beam reflected by the eyeball  30  or the cornea  32  is not expanded. 
     In addition, the diameter (opening) D m  of the effective region of the concave mirror  2  is determined to satisfy the condition of Expression (2). Thus, the diameter D m  of the effective region of the concave mirror  2  can be increased and a laser beam can be converged using a large opening. The diameter of the beam on the light receiving surface of the PSD  3  can be decreased. 
     In this way, the diameter of the laser beam on the light receiving surface of the PSD  3  is decreased, thereby ensuring the position detection resolution by the PSD  3  and the detection accuracy for the pupil position. Thus, the pupil position can be properly detected. 
     The pupil-position detecting device according to the embodiment can be modified in various ways. Modifications of the pupil-position detecting device are described below. 
       FIGS. 8A and 8B  each (first illustration) illustrate an example arrangement of a major part of a pupil-position detecting device according to a first modification,  FIG. 8A  illustrating an arrangement in which an optical path of a laser beam from a VCSEL  1  to a concave mirror  2  intersects with an optical path from an eyeball  30  to a PSD  3 ,  FIG. 8B  illustrating an arrangement in which an optical path of a laser beam from a VCSEL  1  to a concave mirror  2  does not intersect with an optical path from an eyeball  30  to a PSD  3 . 
     An off-axis optical system in  FIG. 8A  includes an optical path  81  (an optical path indicated by a broken line) of a laser beam from the VCSEL  1  to the concave mirror  2 , an optical path  82  (an optical path indicated by a one-dot chain line) from the concave mirror  2  to the eyeball  30  or a cornea  32 , and an optical path  83  (an optical path indicated by a two-dot chain line) from the cornea  32  to the PSD  3 . 
     When the eyeball  30  is in normal vision, the optical path  81 , the optical path  82 , and the optical path  83  are within the same plane, and the optical path  81  intersects with the optical path  83 . The optical paths  81 ,  82 , and  83  may be deviated from the same plane in accordance with the position of a light emitting portion of the VCSEL  1 ; however, the optical paths  81 ,  82 , and  83  are assumed to be included “within the same plane” even in such a case. 
     In  FIG. 8A , the VCSEL  1  is arranged perpendicularly to the optical path  81 , and the PSD  3  is arranged perpendicularly to the optical path  83 . With the arrangement, each optical path length can be increased, and the beam spot of the laser beam on the light receiving surface of the PSD  3  can be prevented from becoming elliptic. Thus, the diameter of the beam can be decreased and the position detection resolution by the PSD  3  can be increased. 
     In contrast, an off-axis optical system in  FIG. 8B  includes an optical path  84  (an optical path indicated by a broken line) of a laser beam from the VCSEL  1  to the concave mirror  2 , an optical path  85  (an optical path indicated by a one-dot chain line) from the concave mirror  2  to the eyeball  30  or a cornea  32 , and an optical path  86  (an optical path indicated by a two-dot chain line) from the cornea  32  to the PSD  3 . The arrangement in  FIG. 8B  is similar to the arrangement in  FIG. 8A  in that the optical paths  84 ,  85 , and  86  are within the same plane. 
     The optical path  84  is arranged in parallel to a reference irradiation plane  90  that is a tangent plane when the inclination of the eyeball  30  in normal vision is zero. The reference irradiation plane  90  is an example of a “reference plane”. With the arrangement, the emission surface of the VCSEL  1  can be made orthogonal to the reference irradiation plane  90 , and the light receiving surface of the PSD  3  and the emitting surface of the VCSEL  1  can be arranged within the same plane. Thus, the VCSEL  1  and the PSD  3  can be arranged on the same substrate, thereby easily mounting the VCSEL  1  and the PSD  3 . 
       FIG. 9  (second illustration) illustrates an example arrangement of a major part of a pupil-position detecting device according to a second modification. 
     Referring to  FIG. 9 , an off-axis optical system includes an optical path  91  (an optical path indicated by a broken line) of a laser beam from a VCSEL  1  to a concave mirror  2 , an optical path  92  (an optical path indicated by a one-dot chain line) from the concave mirror  2  to an eyeball  30  or a cornea  32 , and an optical path  93  (an optical path indicated by a two-dot chain line) from the cornea  32  to a PSD  3 . The optical path  91  intersects with the optical path  93 , and hence the optical path length can be increased. 
     The VCSEL  1  is arranged in an inclined manner with respect to the normal-vision direction of the eyeball  30  indicated by a blank arrow  80  so that a laser beam emitted perpendicularly from the emitting surface is incident on a portion near the center of the concave mirror  2 . 
     Moreover, the VCSEL  1  and the PSD  3  are mounted on a flexible flat cable (FFC)  52  secured to an element support  50 . Since the VCSEL  1  and the PSD  3  are mounted on the same FFC  52 , a power supply line and a signal line can be efficiently arranged. In this case, the FFC  52  is an example of an “electrical substrate”. 
     Furthermore, a drive section including a battery  53  and a circuit group  55  to drive the VCSEL  1  and the PSD  3  is secured on a flexible substrate (flexible printed circuit board, FPC)  51 . FPC  51  is secured on a surface opposite to the mount surface of the VCSEL  1  and the PSD  3  of the element support  50 . The FFC  51  is electrically coupled to the FPC  51  through a connector  54 , thereby saving the space of the drive section. 
     In this case, the circuit group includes a current/voltage (IV) conversion circuit using a trans-impedance amplifier (TIA) or the like, an A/D conversion circuit, a pupil-position estimation circuit, a four-fundamental-operation circuit, an FPGA circuit, and a radio transmission circuit. 
     The PSD  3  is arranged in a direction parallel to the normal-vision direction of the eyeball  30 , and hence the PSD  3  can be easily mounted. Alternatively, the PSD  3  may be arranged such that the light receiving surface is orthogonal to the optical path  93 . Thus, the beam spot of a laser beam on the light receiving surface of the PSD  3  can be prevented from becoming elliptic, the diameter of the beam can be decreased, and the position detection resolution by the PSD  3  can be increased. 
       FIG. 10  (third illustration) illustrates an example arrangement of a major part of a pupil-position detecting device according to a third modification. 
     Referring to  FIG. 10 , an off-axis optical system includes an optical path  94  (an optical path indicated by a broken line) of a laser beam from a VCSEL  1  to a concave mirror  2 , an optical path  95  (an optical path indicated by a one-dot chain line) from the concave mirror  2  to an eyeball  30  or a cornea  32 , and an optical path  96  (an optical path indicated by a two-dot chain line) from the cornea  32  to a PSD  3 . The optical path  94  intersects with the optical path  96 , and hence the optical path length can be increased. 
     In the second modification, the VCSEL  1  is arranged in an inclined manner with respect to the normal-vision direction of the eyeball  30  so that a laser beam emitted perpendicularly from the emitting surface is incident on a portion near the center of the concave mirror  2 . In the modification, a triangular prism  56  is provided between the VCSEL  1  and the concave mirror  2  to deflect a laser beam emitted from the VCSEL  1  so that a laser beam emitted perpendicularly from the emitting surface is incident on the portion near the center of the concave mirror  2 . The triangular prism  56  is an example of a “deflector”. However, the deflector is not limited to the triangular prism  56 , and may be, for example, a diffraction grating. 
     In the second modification, the VCSEL  1  and the PSD  3  are mounted on the FFC  52 . In the modification, the VCSEL  1  and the PSD  3  can be arranged within the same plane. The VCSEL  1  and the PSD  3  are mounted on a FPC  57  secured to an element support  50 . Thus, power supply and mounting of peripheral circuits can be easily performed. Referring to  FIG. 10 , the FPC  57  is secured to one surface of the element support  50 , and the FPC  51  having mounted thereon a battery  53  and a circuit group  55  is secured to a surface opposite to the one surface to which the FPC  57  of the element support  50  is secured. The FPC  51  and the FPC  57  are electrically coupled to each other by a FFC  52 . The FPCs  51  and  57  are each an example of an “electrical substrate”. 
       FIGS. 11A-a  and  11 A-b (fourth-a illustration) each illustrates an example arrangement of a major part of a pupil-position detecting device according to a fourth-a modification,  FIG. 11A-a  being a view from above the major part (in a positive Y direction),  FIG. 11A-b  being a view from the eyeball side (in a positive X direction) of part B (a part surrounded by one-dot chain lines) of  FIG. 11  A-a. 
     In the modification, a package  59 , a battery  53 , and a circuit group  55  are mounted on a circuit board  58  secured to an eyeglass frame  22 . The package  59  includes a cover glass  59   a  and a support frame  59   b,  and houses and seals a VCSEL  1  and a PSD  3  therein. 
     The VCSEL  1  and the PSD  3  are housed in the single package  59 . Thus, the VCSEL  1  and the PSD  3  can be arranged close to each other. Since the package  59 , the battery  53 , and the circuit group  55  are mounted on the single circuit board  58 , a module (inclination position detecting module) including the package  59 , the battery  53 , and the circuit group  55  can be downsized. 
     Furthermore, a radio transmission circuit can be included in the circuit group  55  to wirelessly connect the module to an external terminal, such a smartphone or a tablet. Thus, a detection signal of the PSD  3  can be transmitted to the external terminal through radio transmission to operate the external terminal or collect pupil-position data. 
     In  FIGS. 11A-a  and  11 A-b, the circuit group  55  includes, for example, a light-emission drive circuit, a detection-signal amplification extraction circuit, a pupil-position calculation circuit, and a wireless transmission circuit to implement the respective functions illustrated in  FIG. 6 . In addition, various functions of other circuits such as a circuit for interface with external hardware, a circuit for storage in the memory, a sensor circuit such as an acceleration sensor that determines the orientation of the irradiated surface, and a feedback circuit that controls the operation of the light emission drive circuit are integrally mounted on the circuit group  55 . 
     In this case, the Y direction is an example of the longitudinal direction of the eyeglass-shaped support  20 . The longitudinal direction of the eyeglass-shaped support  20  is, for example, a direction connecting the ear and the nose of a human wearing the eyeglass-shaped support  20 . 
       FIGS. 11B-a ,  11 B-b, and  11 B-c (fourth-b illustration) each illustrates an example arrangement of a major part of a pupil-position detecting device according to a fourth-b modification,  FIG. 11B-a  being a view from above the major part (in a positive Y direction),  FIG. 11B-b  being a view from the eyeball side (in a positive X direction) of part B (a part surrounded by one-dot chain lines) of  FIG. 11B-a , and  FIG. 11B-c  being a view of the part B in  FIG. 11B-a  as viewed from the opposite side of the eyeball. 
     In this modification, the circuit board  58  is fixed to the inner side of the eyeglass frame  22 , the package  59  housing the VCSEL  1  and the PSD  3  is disposed on the eyeball side, and the battery  53  and the circuit group  55  are mounted on the side closer to the outside of the pupil-position detecting device. This arrangement constitutes a double-sided circuit board. The package  59  includes a cover glass  59   a  and a support frame  59   b,  and is sealed containing the VCSEL  1  and the PSD  3  therein. Further, a cover structure made of a resin material of a similar color to the eyeglass frame  22  is provided in the opening located closer to the outside. 
     In this case, the X direction in  FIG. 11B-a  is an example of the thickness direction of the eyeglass-shaped support  20 . The thickness direction of the eyeglass-shaped support  20  is, for example, a direction perpendicular to the normal-vision direction and the direction connecting the ear and the nose of a human wearing the eyeglass-shaped support  20 . 
       FIG. 11B-a  illustrates an example in which the circuit board  58 , the package  59 , the circuit group  55 , and the battery  53  are completely embedded in the eyeglass frame  22 . In this case, these components may be partially embedded in the eyeglass frame  22 . Further, the circuit group  55  may not be provided on exactly back side of the package  59 . 
     With such a configuration, the protrusion of the package  50  portion and the dent of the circuit board installation portion can be eliminated, and an appearance comparable to that of a typical spectacle frame is achieved. Further, the configuration of such a double-sided circuit board can reduce the installation space for the pupil position detecting device according to the present embodiment. 
       FIG. 12  (fifth illustration) illustrates an example arrangement of a major part of a pupil-position detecting device according to a fifth modification. 
     The pupil-position detecting device according to the modification includes a plane mirror  2   a  that reflects a laser beam emitted from a VCSEL  1  toward a concave mirror  2 . An off-axis optical system includes optical paths  97   a  and  97   b  (optical paths indicated by broken lines) of a laser beam from the VCSEL  1  to the concave mirror  2 , an optical path  98  (an optical path indicated by a one-dot chain line) from the concave mirror  2  to an eyeball  30  or a cornea  32 , and an optical path  99  (an optical path indicated by a two-dot chain line) from the cornea  32  to the PSD  3 . The laser beam emitted from the VCSEL  1  reciprocates in a space in front of the eye and then is incident on an eyeball  30 . 
     Since the plane mirror  2   a  is provided, the optical path length from the VCSEL  1  to the concave mirror  2  can be elongated. The following describes some advantageous effects of the elongated optical path. First, the beam diameter of the laser beam reaching the converging reflector can be expanded. In addition, the wavefront of a laser beam can be controlled while the diameter of the beam is expanded. Accordingly, the degree of freedom for design of an optical system and an optical element can be increased. For example, an aspherical shape or an anisotropic shape (such as an anamorphic aspherical surface) can be adopted. Secondly, the distance from the converging reflector disposed in the final stage of the optical system to the eyeball as the irradiation surface can be shortened. In other words, even when the angle of the laser beam incident on the converging reflector is small, a small beam diameter can be obtained on the irradiation surface and the light receiving surface of the PSD by adjusting the length of the optical path to the converging reflector. Third, the change in the position of the beam spot on the light receiving surface of the PSD can be controlled. Such a change in the position of the beam spot depends on the rotation angle of the eyeball. By designing the length of the optical path so that the size of the light receiving surface of the PSD fits into the measurement range of the rotation angle of the eyeball, a pupil-position detecting device having desired viewing angle and angular resolution can be provided. 
     The plane mirror  2   a  and the concave mirror  2  may be arranged in a reversal manner. Instead of the plane mirror  2   a,  a second concave mirror may be provided. However, it is desirable to properly set the curvature radius of the concave mirror  2  and to properly arrange the plane mirror  2   a  and the concave mirror  2  so that the laser beam after being reflected by the eyeball  30  or the cornea  32  becomes parallel light as illustrated in  FIGS. 3A and 3B . 
     A pupil-position detecting device according to a sixth modification includes a position adjustor  131  that adjusts the position of a concave mirror  2 , and an inclination adjustor  132  that adjusts the inclination of the concave mirror  2 . 
       FIGS. 13A and 13B  each (sixth illustration) illustrate an example arrangement of a major part of the pupil-position detecting device according to the modification,  FIG. 13A  being a view of the concave mirror  2  from a side facing the concave surface,  FIG. 13B  being a cross-sectional view taken along line A-A′ in  FIG. 13A . 
     As illustrated in  FIG. 13A , the position adjustor  131  includes setscrews  131   a,    131   b,  and  131   c,  and a frame portion  131   d.  The setscrews  131   a,    131   b,  and  131   c  constitute a three-point support mechanism that supports three points of a side surface portion of the concave mirror  2 . The setscrews  131   a  to  131   c  are independently advanced and retracted to change the position of the concave mirror  2  within a YZ plane and the inclination of the concave mirror  2  within the YZ plane. 
     As illustrated in  FIG. 13B , the inclination adjustor  132  includes a substrate  132   a,  a spring  132   b,  and a setscrew  132   c.  The substrate  132   a  is a plate-shaped member having a plane portion defined by the YZ plane, and has a protruding portion  133  at the center of the plane portion. The protruding portion  133  has a tip end in a negative X direction. The tip end is in contact with a surface on a side in the negative X direction included in the frame portion  131   d  of the position adjustor  131 . 
     The spring  132   b  is provided at each of two positions in the Y direction of the substrate  132   a.  The springs  132   b  gives the concave mirror  2  urging forces in the negative X direction. The substrate  132   a  and the frame portion  131   d  are coupled to each other by the springs  132   b.    
     The setscrew  132   c  is provided at one position in the Y direction. When the setscrew  132   c  advances in the negative X direction and presses the concave mirror  2  via the frame portion  131   d,  the concave mirror  2  can be inclined (can ascend) in an out-of-plane direction of the YZ plane using the principle of the lever while the tip end of the protruding portion  133  serves as a fulcrum. 
     To further finely adjust the inclination of the concave mirror  2  in the out-of-plane direction of the YZ plane, the two positions of the springs  132   b  are desirably farther from each other in the Y direction as much as possible. The position of the setscrew  132   c  is desirably closer to an end portion of the substrate  132   a  in the Y direction. 
     The mechanism in which the setscrew  132   c  is provided at the one position in the Y direction and the concave mirror  2  is inclined around the Z axis has been described. However, a setscrew may be additionally provided at one position in the Z direction so that the concave mirror  2  can be inclined about the Y axis. 
     In the modification, the position adjustor  131  and the inclination adjustor  132  are used to adjust the position and inclination of a laser beam to be emitted from the concave mirror  2  to an eyeball  30  or a cornea  32 . 
     The position adjustor and the inclination adjustor for the concave mirror  2  are illustrated in  FIGS. 13A and 13B . However, even when an optical element such as a diffraction element is provided instead of the concave mirror  2 , similar adjustors can adjust the position and inclination of the optical element. 
       FIGS. 14A and 14B  each (seventh illustration) illustrate an example arrangement of a major part of a pupil-position detecting device according to a seventh modification,  FIG. 14A  being a view from above the major part (in the positive Y direction),  FIG. 14B  being a view from the eyeball side (in the positive X direction) of part C (a part surrounded by one-dot chain lines) of  FIG. 14A . 
     As illustrated in  FIGS. 14A and 14B , the pupil-position detecting device according to the modification includes a light guide  150  disposed between a VCSEL  1  and a concave mirror  2  at a position in front of an eye of a person who wears an eyeglass-shaped support  20 . The light guide  150  allows light to propagate thereinside to guide a laser beam emitted from the VCSEL  1  to the concave mirror  2 . 
     The light guide  150  is, for example, a transparent cylindrical member. Light emitted from the VCSEL  1  is incident on an end surface in the negative X direction of the light guide  150  into the light guide  150 , passes through the inside of the light guide  150 , and is incident on a reflecting curved surface  150   a  formed on an end surface in the positive X direction of the light guide  150 . The reflecting curved surface  150   a  is a surface that functions as a concave mirror. The reflecting curved surface  150   a  can reflect an incident laser beam to emit a convergent laser beam toward an eyeball  30 . 
     The word “transparent” of the light guide  150  represents being transparent to visible light and light emitted from the VCSEL  1 . Being transparent to visible light allows a person wearing the eyeglass-shaped support  20  to visually recognize the front without the sight being interrupted by the light guide  150 . Being transparent to light emitted from the VCSEL  1  decreases a loss due to light absorption and allows the light to propagate thereinside. The light guide  150  is not limited to a cylindrical member, and may have any cross-sectional shape as far as being columnar member. 
     As illustrated in  FIGS. 14A and 14B , the light guide  150  is supported by a light-guide support  151 . The light-guide support  151  is secured to a circuit-board support  58   a  that supports a circuit board  58  on which the VCSEL  1  and a PSD  3  are mounted. The VCSEL  1 , the concave mirror  2 , and the PSD  3  are supported while their positional relationship is fixed as an L-shaped structure. 
     The light-guide support  151  and the circuit-board support  58   a  can be rotated in a direction of an outer periphery of the cylindrical shape, and can be advanced and retracted in an optical-axis direction. Thus, the position at which the laser beam reflected by the reflecting curved surface  150   a  of the end portion of the light guide  150  is incident on the eyeball  30  or a cornea  32  can be adjusted. 
     The light-guide support  151  has an opening to prevent the positions of the VCSEL  1  and the PSD  3  mounted on the circuit board  58  from changing due to the positional adjustment of the light-guide support  151 . 
     In the pupil-position detecting device according to the modification, optical elements such as the VCSEL  1 , the light guide  150 , and the PSD  3  can be integrally formed, thereby downsizing the pupil-position detecting device. 
     A pupil-position detecting device according to an eighth modification includes a non-coaxial concave mirror  2   b  instead of the concave mirror  2 . 
       FIG. 15  illustrates an example arrangement of the non-coaxial concave mirror  2   b.  The non-coaxial concave mirror  2   b  includes an axisymmetric shape with respect to a center axis D indicated by a broken line in  FIG. 15 . The non-coaxial concave mirror  2   b  includes two curved surfaces provided at positions symmetrical to each other with respect to the center axis D and having curvature centers at positions different from each other. 
     More specifically, as illustrated in  FIG. 15 , the non-coaxial concave mirror  2   b  includes a curved surface  2   b   1  and a curved surface  2   b   2  at positions symmetrical to each other with respect to the center axis D. The curved surface  2   b   1  has a curvature center  2   b   21  and the curved surface  2   b   2  has a curvature center  2   b   22 , at positions deviated from each other in a direction intersecting with the center axis D. The curved surface  2   b   1  and the curved surface  2   b   2  may each have any one of a spherical surface and an aspherical surface. 
     The shapes of the curved surfaces  2   b   1  and  2   b   2  of the non-coaxial concave mirror  2   b  are properly set to convert a laser beam reflected by an eyeball  30  or a cornea  32  into a non-diffracted beam and causes the non-diffracted beam to propagate to the PSD  3 . The non-diffracted beam is, for example, a vessel beam or the like having a concentric beam profile. 
       FIG. 16  illustrates an example of a non-diffracted beam. A divergent laser beam emitted from the VCSEL  1  is converted into a convergent laser beam by the non-coaxial concave mirror  2   b,  and is incident on an eyeball  30  or a cornea  32 . 
     With the non-coaxial concave mirror  2   b  in  FIG. 16 , a laser beam L 3  indicated by a solid line and a laser beam L 4  indicated by a broken line propagate as two parallel laser beams at slightly different angles after reflection by the eyeball  30  or the cornea  32  in a view within a two-dimensional plane (in an actual three-dimensional space, rays have equivalent projection components on the optical axis and have equivalent wave vectors directed inward in the same radial direction). 
     Such laser beams have a beam profile of a Bessel function as a result of an interference with light having a wave vector component facing the optical axis in an oblique hatching region in  FIG. 16 . Moreover, a beam can propagate by a long distance in the optical-axis direction without the diameter of the beam being changed. 
     A laser beam L 5  (a part with oblique hatching) that is incident on the light receiving surface of the PSD  3  serves as a non-diffracted beam. Thus, the mount position of the PSD  3  can be made robust. The formation region of the non-diffraction beam may be at a position before the laser beam is reflected by the eyeball  30 . In this case, robustness of the position of the eyeglass-shaped support  20  can be increased. 
     A pupil-position detecting device according to a ninth modification includes a holographic optical device (HOE)  2   c  instead of the concave mirror  2 . The HOE is an example of a “diffraction reflector”. 
       FIGS. 17A-a  and  17 A-b illustrate an example arrangement of an off-axis optical system using a HOE,  FIG. 17A-a  illustrating a case where a HOE  2   c  generates one convergent laser beam,  FIG. 17A-b  illustrating a case where a HOE  2   d  generates a plurality of convergent laser beams. The HOEs  2   c  and  2   d  are each an example of a “converging reflector”, and an example of a “diffraction reflector”. 
     A HOE can reflect light perpendicularly incident on a plane to an inclined direction. Thus, as illustrated in  FIG. 17A-a , the HOE  2   c  can be disposed so that the plane portion faces the emitting surface of the VCSEL  1  while a laser beam is emitted on an eyeball  30 . Thus, positioning can be easily performed during mounting. In addition, the HOE  2   c  can be fabricated thinner, thereby downsizing the pupil-position detecting device. 
     Alternatively, a plurality of convergent laser beams can be generated from a laser beam emitted by one light emitting portion of the VC SEL  1 . The convergent laser beams can be simultaneously emitted at a plurality of positions of an eyeball  30 .  FIG. 17A-b  illustrates an example in which three convergent laser beams are generated, the beams including a 0-th order beam L 90 , a +1st order diffracted beam L 91 , and a −1st order diffracted beam L 92  by the HOE  2   d.    
     Referring to  FIGS. 2A and 2B , for a large rotation movement of the eyeball  30 , the light emitting portion of the VCSEL  1  is shifted to expand the detection range. In the modification, the number of convergent positions by one light emitting portion of the VCSEL  1  can be three. Thus, even when the eyeball  30  performs a larger rotation movement, the laser beam reflected by the eyeball  30  or a cornea  32  can be prevented from being deviated from the light receiving surface of the PSD  3 , and the detection range for the rotation angle can be expanded. 
     Alternatively, a diffractive optical element (DOE) or a Fresnel lens may be used instead of the HOE. 
     A pupil-position detecting device according to a tenth modification includes a first reflective condenser element  200  including a liquid crystal portion  202  including an anisotropic molecular material enclosed therein instead of the concave mirror  2 . In this case, the anisotropic molecular material represents a liquid crystal material or the like. 
       FIG. 17B  illustrates an example arrangement of an off-axis optical system using the first reflective condenser element  200 . As illustrated in  FIG. 17B , the first reflective condenser element  200  includes a support substrate  201 , the liquid crystal portion  202 , and a ¼ wave shift portion  203 . The first reflective condenser element  200  is an example of a “converging reflector”. The liquid crystal portion  202  is an example of an “enclosure portion”. 
     Linear polarized light emitted from a VCSEL  1  is converted by the ¼ wave shift portion  203  into circular polarized light, and is incident on the liquid crystal portion  202 . Light reflected by the liquid crystal portion  202  toward an eyeball  30  passes through the  1 / 4  wave shift portion  203  in a direction opposite to the incoming direction, is converted into linear polarized light again, and is incident on the cornea surface of the eyeball  30 . Then, light reflected by the cornea surface is incident on a PSD  3 . 
     As illustrated in  FIG. 17C , the liquid crystal portion  202  includes a support substrate  2021 , an oriented film  2022 , an oriented film  2023 , and a transmissive support substrate  2024 . 
     The space inside the films defined by the oriented film  2022  and the oriented film  2023  contains liquid crystal molecules  2025 . The liquid crystal molecules  2025  are arrayed while being rotated in a spiral form in a direction perpendicular to the surfaces of the oriented films  2022  and  2023 . 
     The oriented films  2022  and  2023  spatially control the orientation of the liquid crystal molecules  2025 . Specifically, the inner sides of the surfaces of the oriented films  2022  and  2023  are each divided into very small spatial regions, each region is irradiated with ultraviolet (UV) light polarized in a specific direction, and oriented is provided to control the orientation of the liquid crystal molecules  2025  per small spatial region. 
     In other words, the liquid crystal molecules  2025  are oriented to form a three-dimensional quasi-periodic structure inside the liquid crystal portion  202 . The quasi-periodic structure represents a structure in which the structural period or the phase of the structural period is spatially adjusted to exhibit condensing characteristics. 
     Light incident on the liquid crystal portion  202  in a direction from the right to the left in  FIG. 17C  passes through the transmissive support substrate  2024  and the oriented film  2023 , is reflected by the action of the liquid crystal molecules  2025 , passes through the oriented film  2023  and the transmissive support substrate  2024  in a direction opposite to the incoming direction, and is emitted from the liquid crystal portion  202 . 
     In the example in  FIG. 17C , the orientation on the surface of the oriented film  2022  or  2023  corresponding to the start position of the spiral structure by the liquid crystal molecules  2025  is adjusted. With the adjustment, an equiphase surface  2026  of a curved line indicating the spiral structure is curved in a concave surface shape with respect to the incidence direction of light. Thus, the liquid crystal molecules  2025  function as a lens, and hence the light reflected by the action of the liquid crystal molecules  2025  and propagating in the right direction of the drawing can be condensed. A technology of causing liquid crystal molecules to function as an optical element such as a lens may use a known technology (for example, see Nature Photonics Vol. 10 (2016) p. 389), and further detailed description is omitted here. In  FIG. 17C , one-dot chain lines indicate light  2027  that is incident on the liquid crystal portion  202 , and two-dot chain lines indicate light  2028  that is reflected by the liquid crystal portion  202  and that is condensed. 
     The optical characteristics of the liquid crystal portion  202  are further described next referring to  FIGS. 17D-a  and  17 D-b.  FIG. 17D-a  and  FIG. 17D-b  illustrate the liquid crystal portion  202  that condenses rightward circular polarized light. The liquid crystal portion  202  has reflection characteristics or transmission characteristics that are provided for rightward polarized light and leftward polarized light depending on the rotation direction of the liquid crystal molecules  2025 . 
     In  FIG. 17D-a , light converted by the ¼ wave shift portion  203  into circular polarized light is incident on the liquid crystal portion  202 . Light reflected by the liquid crystal portion  202  passes through the ¼ wave shift portion  203  again in a direction opposite to the incoming direction to be returned into linear polarized light, and is emitted on the eyeball  30 . To minimize emission of a laser beam on the eyeball  30 , linear polarized light is desirably S-polarized light having an electric field vibration surface in a direction perpendicular to the paper face of the drawing. 
       FIG. 17D-b  illustrates an example of random polarized light in which polarization of a ray from the VCSEL  1  is not controlled. Rightward circular polarized light included in the random polarized light incident on the liquid crystal portion  202  is reflected and condensed by the support substrate  2021 , passes through the ¼ wave shift portion  203 , and is converted into linear polarized light. In contrast, a leftward polarized light component directly passes through the support substrate  201 , and is not emitted on the cornea surface. 
     With the pupil-position detecting device according to the modification, three-dimensional orientation distribution of the liquid crystal molecules  2025  can be controlled by two-dimensional orientation control on the oriented films  2022  and  2023 . Thus, the first reflective condenser element  200  that is thin and has high reflection and diffraction efficiencies can be provided. Moreover, the first reflective condenser element  200  can have polarization selectivity. A pupil-position detecting device that attains both a decrease in the number of optical components and safety of eyes against laser beams can be provided. 
     A pupil-position detecting device according to an eleventh modification includes a second reflective condenser element  210  including an anisotropic molecular material. 
       FIG. 17E  illustrates an example arrangement of an off-axis optical system using the second reflective condenser element  210 . As illustrated in  FIG. 17E , the second reflective condenser element  210  includes a liquid crystal portion  211 , a light guide  212 , and a ¼ wave shift portion  213 . The second reflective condenser element  210  is an example of a “converging reflector”. The liquid crystal portion  211  is an example of an “anisotropic molecular material portion”. 
     The liquid crystal portion  211  is provided in contact with the interface of a light guide region of the light guide  212 . Similarly to the above-described liquid crystal portion  202 , liquid crystal molecules are oriented to form a three-dimensional quasi-periodic structure in the liquid crystal portion  211 . 
     Light emitted from a VCSEL  1  is coupled in the light guide  212  via an inclined surface at an incidence end of the light guide  212 . The light may be coupled in the light guide  212  through grating; however, it is desirable to employ an arrangement in which the mount substrate surface of the VCSEL  1  is orthogonal to the light guide  212  with regard to convenience and accuracy of mounting. 
     Light coupled in the light guide  212  is repetitively totally reflected by the interface of the light guide  212 , and propagates in the light guide  212  to a position in front of an eye. Rightward circular polarized light or leftward circular polarized light included in the light propagating inside the light guide  212  is selectively reflected by the liquid crystal portion  211 , is condensed by a lens function of the liquid crystal portion  211 , is converted into linear polarized light (S-polarized light) by the ¼ wave shift portion  213 , and then is emitted on the cornea surface of an eyeball  30 . 
     When the light guide  212  is used, it is difficult to irradiate the cornea surface with light at a small angle, and hence light is reflected by the liquid crystal portion  211  at a position near the front surface of the eyeball  30 . In this case, to allow light to be incident on a PSD  3 , the light is required to be condensed at a position shifted from the pupil center position on the cornea toward the PSD  3  (specular reflection position). 
     With the pupil-position detecting device according to the modification, the light emitted from the VCSEL  1  can be emitted on the cornea surface while the optical path length is ensured in the light guide  212 , thereby downsizing the pupil-position detecting device. Moreover, a configuration of a housing like  FIGS. 14A and 14B  can be employed so that the VCSEL  1 , the light guide  212 , and the PSD  3  are integrally formed. 
     A retinal projection display  60  according to a second embodiment is described next referring to  FIG. 18 . 
       FIG. 18  illustrates an example arrangement of the retinal projection display  60  according to the embodiment. 
     The retinal projection display  60  includes a red, green, and blue (RGB) laser source  61 , a scanning mirror  62 , a plane mirror  63 , a half mirror  64 , an image generator  65 , and a pupil-position detecting device  10 . 
     The RGB laser source  61  modulates laser beams of three RGB colors in terms of time, and outputs the modulated laser beams. The scanning mirror  62  performs two-dimensional scanning with light from the RGB laser source  61 . The scanning mirror  62  is a micro-electromechanical systems (MEMS) mirror or the like. However, the scanning mirror  62  is not limited thereto, and may be any configuration including a reflecting portion that provides scanning with light, such as a polygon mirror or a galvano-mirror. The MEMS mirror is more advantageous to decrease the size and weight. The driving system of the MEMS mirror may employ any system, such as an electrostatic system, a piezoelectric system, or an electromagnetic system. 
     The plane mirror  63  reflects scanning light from the scanning mirror  62  toward the half mirror  64 . The half mirror  64  transmits a portion of incident light and reflects another portion of the incident light toward an eyeball  30 . The half mirror  64  has a concave curved-surface shape. The half mirror  64  causes the reflected light to converge to a portion near a pupil  31  of an eyeball  30  and to be focused at a position of a retina  33 . Thus, an image formed with scanning light is projected on the retina  33 . Light  51   a  indicated by broken lines in the drawing represents light to form an image on the retina  33 . The ratio of the light intensity of reflected light to the light intensity of transmitted light provided by the half mirror  64  does not have to be 1:1. 
     The pupil-position detecting device  10  detects the position of the pupil  31  in accordance with an eyeball movement, and transmits a feedback signal for the position of the pupil  31  to the image generator  65 . 
     The image generator  65  has a deflection angle control function for the scanning mirror  62  and a light emission control function for the RGB laser source  61 . Moreover, the image generator  65  receives the feedback signal for the position of the pupil  31  from the pupil-position detecting device  10 . The deflection angle of the scanning mirror  62  and the light emission of the RGB laser source  61  are controlled in accordance with the position of the pupil  31  detected by the pupil-position detecting device  10 , to re-write a projection angle of an image or an image content. Thus, an image tracking (eye-tracking) a change in the position of the pupil  31  due to the eyeball movement can be formed on the retina  33 . 
     In the above description, the retinal projection display  60  is, for example, a head-mounted display (HMD) that is a wearable terminal. However, the retinal projection display  60  is not limited to an apparatus that is directly mounted on the head of a “person”, and may be an apparatus that is indirectly mounted on the head of a “person” via a member such as a securing portion (head-mounted display). Alternatively, a binocular retinal projection display including a pair of retinal projection displays  60  for left and right eyes may be used. 
     A device according to a comparative example and the pupil-position detecting device  10  according to the embodiment are compared to each other. The device according to the comparative example uses a laser source to perform scanning with a laser beam using a MEMS mirror, and changes the incident angle of light on an eyeball. In contrast, according to the embodiment, a VCSEL including a plurality of light emitting portions serves as a light source, and the incident angle of light on an eyeball is changed by changing a light emitting portion of the VCSEL. With the embodiment, the incident angle of light on the eyeball is changed without using a movable portion. Thus, compared to a configuration with a movable portion, the configuration according to the embodiment is resistant to, for example, a vibration or an external shock. 
     The device according to the comparative example detects the intensity of reflected light of light emitted on a cornea using a photodetector. In contrast, the device according to the embodiment uses a PSD to detect the position of light that is reflected by an eyeball and is incident on a light receiving surface of the PSD. The PSD detects the position of incident light irrespective of the light intensity. Even when the intensity of reflected light varies due to the reflected position of light on the eyeball, the position can be detected with high sensitivity without an influence of the difference in the intensity of reflected light. Consequently, the inclination position of the eyeball, such as the inclination position of the pupil, can be detected with high accuracy. 
     According to the embodiment, the light-emission drive unit  110  is provided. The light-emission drive unit  110  individually turns on light while the light-emission drive unit  110  shifts the position of the light emitting portion of the VCSEL and the light emission timings among the light emitting portions. Thus, a rough movement of an eyeball is obtained to allow reflected light from the eyeball to be within the light receiving surface of the PSD, and a fine motion of the eyeball movement can be obtained by position detection by the PSD. 
     With the device according to the comparative example, the eyeball position is estimated based on the two peak intensities on the time axis of the reflected light at the eyeball (two reflected positions on the cornea). In this embodiment, the eyeball position is estimated based on a single reflected position on the eyeball such as the cornea. Thus, the VCSEL and the PSD may not be disposed at symmetric positions. In this embodiment, the PSD may not be disposed at a position near a regular reflection (mirror reflection) angle of the eyeball, and may be disposed on the same side as the VCSEL. 
     Although the embodiments of the present disclosure have been described above, the present disclosure is not limited to such specific embodiments, and various modifications and changes can be made without departing from the spirit and scope of the present disclosure as set forth in the appended claims. 
     Information on the pupil position detected by the pupil-position detecting device  10  may be used for eye-tracking to be performed by an input device of an electronic apparatus. For example, an output of the pupil-position detecting device  10  illustrated in  FIG. 1  may be used for eye-tracking as input information to an electronic apparatus. Thus, eye-tracking robust for a positional shift of the head can be provided. 
     The disclosure may be also employed for an optometric apparatus having a function of detecting an inclination of an eyeball or a pupil position (cornea). The optometric apparatus represents an apparatus capable of performing various inspections, such as an eyesight inspection, an ocular refractive-power inspection, an ocular tension inspection, and an ocular axial length inspection. The optometric apparatus is an apparatus that can inspect an eyeball in a non-contact manner. The optometric apparatus includes a support that supports the face of a subject, an ocular inspection window, a display that provides displaying to cause the direction of the eyeball of the subject (the direction of line of sight) to be constant during the ocular inspection, a controller, and a measurement section. It is required for the subject to look at a single point without moving the eyeball (line of sight) to increase measurement accuracy of the measurement section. The subject fixes the face to the support portion, and gazes at a displayed object displayed on the display through the ocular inspection window. At this time, when the inclination position of the eyeball is detected, an inclination-position detecting device for an eyeball according to the embodiment can be used. The inclination-position detecting device for the eyeball is disposed on a lateral side of the measurement section not to interrupt measurement. Information on the inclination position (line of sight) of the eyeball obtained by the eyeball inclination-position detecting device can be fed back to the controller and can perform measurement in accordance with the inclination-position information. 
     Each of the functions of the described embodiments may be implemented by one or more processing circuits or circuitry. Processing circuitry includes a programmed processor, as a processor includes circuitry. A processing circuit also includes devices such as an application specific integrated circuit (ASIC), DSP (digital signal processor), FPGA (field programmable gate array) and conventional circuit components arranged to perform the recited functions. 
     Numerous additional modifications and variations are possible in light of the above teachings. It is therefore to be understood that, within the scope of the above teachings, the present disclosure may be practiced otherwise than as specifically described herein. With some embodiments having thus been described, it will be obvious that the same may be varied in many ways. Such variations are not to be regarded as a departure from the scope of the present disclosure and appended claims, and all such modifications are intended to be included within the scope of the present disclosure and appended claims.