Abstract: A Fresnel lens comprises at least one first prism and one second prism. Each prism has a first side and a second side which forms with a main axis an angle greater than that formed by the first side and the main axis. Conventionally, the second side of the first prism collimates the light received from a light source in line with the main axis. In order to improve the optical effectiveness, the second side of the second prism transmits the light received from the source in a first direction slightly different from the main axis.

Abstract: A transparent screen is constructed in such a way that a plurality of Fresnel prisms 12d each of which is smaller than a plurality of Fresnel prisms 12a and has a shape approximately similar to that of each of the plurality of Fresnel prisms 12a are arranged in a sawtooth shape on a non-light incidence surface portion of a Fresnel lens 12 on a light incidence side to which any image light PB applied from a projector 1 is not applied directly because blocked by a Fresnel prism 12a placed frontwardly.

Abstract: Various embodiments related to rear-projection image display are disclosed. For example, one disclosed embodiment provides a projector for projecting an image and a screen configured to display the image. The screen comprises a filter layer having a light reception side and an image display side. The filter layer includes an array of trapezoidal transmissive elements and an array of trapezoidal absorption elements, where a wider base of each of the trapezoidal transmissive elements faces the light reception side of the filter layer, and where a wider base of each of the trapezoidal absorption elements faces the image display side of the filer layer.

Abstract: A method for generating spontaneously aligned surface wrinkles utilizes control of local moduli-mismatch and osmotic pressure. The method includes modifying the surface of an elastomeric layer to form a superlayer that is stiffer and/or less absorbent than the elastomeric layer. The elastomeric layer is then swollen with a polymerizable monomer, which causes buckling of the superlayer. The monomer is then polymerized, dimensionally stabilizing the surface buckling. The buckled surfaces generated by the method are useful in a wide variety of end-use applications, including microlenses, microlens arrays, compound microlenses, diffraction gratings, photonic crystals, smart adhesives, mechanical strain sensors, microfluidic devices, and cell culture surfaces.

Abstract: The present method for coating a Fresnel lens blank includes providing an uncoated Fresnel lens blank having a structure surface and a non-structured surface, providing a transparent mold part having molding surface substantially matching the base curvature of the Fresnel lens, depositing a metered quantity of coating resin between the molding surface and the structured surface of the Fresnel lens, applying pressure between the Fresnel lens and the mold part while maintaining the distance between the molding surface and the structure surface so that the thickness of the coating is greater than 1.5 times the Fresnel structural height of the structured surface and less than 5 times of the Fresnel structure height of the structured surface and curing the resin coating in situ by directing the incident UV radiation at the Fresnel lens. A double coating may be employed for obtaining both higher optical power and better mechanical properties.

Abstract: A non-imaging lens includes a transparent member, a first Fresnel lens portion and a second Fresnel lens portion. The transparent member includes a first surface and a second surface. The first Fresnel lens portion includes a plurality of first saw-toothed protrusions concentrically defined on the first surface. The second Fresnel lens portion includes a plurality of second saw-toothed protrusions concentrically defined on the first surface. The second saw-toothed protrusions are defined around the first saw-toothed protrusions. Each of radii of curvature of the second saw-toothed protrusions is different from each of radii of curvature of the first saw-toothed protrusions.

Abstract: A Fresnel optical element has a plurality of slopes that refract or reflect light, and the variation of the slope angle between adjacent slopes is constant.

Abstract: A light concentrator is described, for a device for the conversion of solar radiation into electrical, thermal or chemical energy, capable of conveying the radiation towards a surface of the conversion device. The concentrator comprises at least one portion of Fresnel lens of rotational symmetry, one face of which has a plurality of crests disposed concentrically about a center so as to form a segmented transverse profile of the portion of Fresnel lens. The profile is formed in such a manner that the focal distance of the Fresnel lens is variable in dependence on the radial distance from the center of the lens. The variation of the focal distance is determined such that, when the Fresnel lens is illuminated by polychromatic radiation, the superposition of the distributions of irradiance, produced by the lens at the individual wavelengths constituting the spectrum of the incident radiation, generates a substantially uniform distribution of polychromatic irradiance on the conversion device.

Abstract: Apparatus for concentrating light rays arriving from at least one opening onto a receiver, individual beams of the light rays each arriving at the apparatus substantially collimated, the apparatus including a respective Fresnel lens assembly for each opening, the Fresnel lens assembly including a first Fresnel lens, and a second Fresnel lens, the first Fresnel lens being located between the opening and the receiver, the second Fresnel lens being located between the first Fresnel lens and the receiver, the first Fresnel lens collimating the light rays arriving from the opening, the second Fresnel lens converging the collimated light rays onto the receiver, the opening being located in front of the Fresnel lens assembly, on the focal plane of the first Fresnel lens, centered on the focal point of the first Fresnel lens, and the receiver being located behind the Fresnel lens assembly, on the focal point of the second Fresnel lens.

Abstract: There is provided means of achieving the improvement of optical coupling efficiency between a surface receiving/emitting element and an optical transmission path with a simple structure and low cost. An optical element and a substrate having an optical waveguide layer and electric wiring are connected with each other through a lens having a Fresnel lens shape. A through via is provided in the lens, and the optical element and the electric wiring in the substrate are electrically connected with each other through the through via. Instead of the lens, a unit in which a lens is mounted inside an optical-element mounting substrate may be used.

Abstract: Methods and apparatus to correct a curved Petzval focusing surface to a plane using a convex lens, a concave lens, and a space arranged between the curved side of the convex lens and the curved side of the concave lens. The method and apparatus may also include a Fresnel lens arranged between the concave lens and a pixel array.

Abstract: A micro-optic lens is disclosed. The micro-optic lens includes a substrate; and a lens element on the substrate, wherein the lens element includes a flat surface and an annularly grooved surface including first facets and second facets, and wherein the first facets collimate a light effectively and the second facets are parallel to a light. The micro-optic lens can decrease the draft loss and collimate the emitted light beams to increase the light efficiency. Further, the present invention also provides a method for designing angles of micro-optic lenses.

Abstract: An exemplary Fresnel lens includes a flat emitting surface and a plurality of annular Fresnel lens elements at an opposite side thereof to the emitting surface. Each of the Fresnel lens elements has a non-lens surface perpendicular to the emitting surface and a Fresnel lens surface adjoining the non-lens surface with an acute angle. Each of the Fresnel lens elements has a plurality of spaced cavities defined in the non-lens surface.

Abstract: A non-imaging lens includes a transparent member, a conical protrusion and a plurality of annular protrusions. The transparent member includes a first surface and a second surface. The first surface and the second surface are planar. The conical protrusion is defined on the first surface. The annular protrusions are concentrically defined on the first surface around the conical protrusion. Each of cross-sections of the annular protrusions approximately forms a right-angled triangle. The triangle includes a first angle, a second angle, a bottom surface, a first surface and a second surface. The first angle exceeds the second angle. The first angle is less than or equal to 90°. The bottom surfaces of the triangles increase in turn outwards from the conical protrusion.

Abstract: An optical sheet receiving an incident light from a light source is provided. The optical sheet includes a body, a plurality of reflective structures, and a plurality of Fresnel lens units. The body includes an incident surface and an emergent surface. The incident surface receives the incident light with an incident angle. The refractive index of the body is ni and i is a positive integer. The reflective structures are placed on the body. There is a spacing W between two neighboring reflective structures. In the direction of the incident light, the thickness of the reflective structure is t. The Fresnel lens units, having a width P, are disposed on the emergent surface. Each Fresnel lens is corresponded to the spacing. When the equation, tan?1 [P2/6t]>sin?1 ?i=1j1/ni,j?1, is satisfied, the incident light passes through the spacing, the incident angle is adjusted by the thickness t and converged by the Fresnel lens units.

Abstract: A point focus thin film Fresnel lens (15; 25) has an inner, substantially flat region (8; 22), and an outer region (9; 23), the outer region projecting outwardly from the inner region and at a substantial angle away from the plane of the inner region. In one embodiment the lens is in the form of a truncated cone (15) with a circular inner region as its apex, hi another embodiment the lens is in the form of a dome (25) and the outer region is formed by joining together segments (23) extending radially from a circular central region (22).

Abstract: The present invention provides A Fresnel lens sheet for use in a luminaire, comprising a transparent sheet having a first surface on one side which is substantially planar and a second surface on the other side; and a Fresnel lens part containing a plurality of concentric convex prisms formed on the second surface, each of the convex prisms having a cross-section of substantially triangular structure, wherein the substantially triangular structure has an apex formed by joining a first curved portion and a second curved portion, and a base; and this triangular structure has a ratio of a radius of the second curved portion to a base width ranging from 0.1 to 0.5. The invention also provides a luminaire utilizing the Fresnel lens sheet of the invention.

Abstract: A non-imaging lens includes a transparent member, a conical protrusion, and a plurality of annular protrusions. The transparent member includes a first surface and a second surface. The first surface and the second surface are planar. The conical protrusion is defined on the first surface of the transparent member. The annular protrusions are concentrically defined on the first surface around the conical protrusion. Each of cross-sections of the annular protrusions approximately forms a right triangle. Each of the triangles includes a first angle, a second angle, a bottom surface, a first surface and a second surface. The first angle exceeds the second angle. The first angle is less than or equal to 90°. The second angles increase in turn outwards from the conical protrusion. The width of the bottom surface is equal to the radius of the conical protrusion.

Abstract: The invention relates to a device and a method for producing resist profiled elements. According to the invention, an electron beam lithography system is used to produce an electron beam, the axis of the beam being essentially perpendicular to a resist layer in which the resist profiled element is to be produced. The electron beam can be adjusted in terms of the electron surface dose in such a way that a non-orthogonal resist profiled element can be produced as a result of the irradiation by the electron beam.

Abstract: A method for forming a laminated product includes providing a film (2) having a first surface embossed with optical structures and an opposite second surface; guiding the film to a nip point of a pair of lamination rolls (5, 6); feeding a polymer sheet (4) to the nip point (7), wherein the polymer sheet has a surface temperature effective to enable thermal bonding between the polymer sheet and the film; and laminating the polymer sheet to the second surface of the film. The present process reduces the cost and environmental impact associated with laminating fresnel lens film to acrylic sheet versus existing industry technology.

Abstract: The Fresnel lens sheet according to the present invention has a plurality of prismatic Fresnel lens elements including a Fresnel facet, a riser facet, and a top facet crossing the facet and the riser facet on an entrance surface. An angle of the top facet of each Fresnel lens element constituting the lens relative to the an exit surface, ?1, is determined so that an exit angle of the light that has entered each of the top facets and exits from the exit surface, ?, is greater than 35 degrees.

Abstract: This invention deals with novel method and apparatus for positioning and motion control of the optical elements (mirrors and lenses) of a Fresnel solar concentrator tracking array which approximately eliminates gravitational torque by use of a central universal pivot or gimbals. Linkage torque is produced by induced and/or permanent dipole coupling to an electronic grid to produce angular deflection, and rotational motion that is enhanced by the presence of highly polarizable material. This system is ideally suited for maximization of solar energy focused by the array onto a receiver. Since there are no mechanical linkages, the instant invention is applicable for fabrication from the mini- to the nano-technology realm. The elimination of gravitational torque by balancing the optical elements on a universal pivot or gimbals greatly reduces the power required for the optical elements to track the sun and focus sunlight onto a receiver.

Abstract: Disclosed is a LED curing light device for curing of photo-polymerization materials. The device has a plurality of LED sources and a plurality of Fresnel lenses. The LED source is powered and controlled by a drive board and batteries providing high power curing light in the range of 300 to 500 nm and optical power in the range of 100 to 800 mW.

Abstract: An autofocus system is provided for image capture that includes a liquid crystal focus lens which includes a dual range liquid crystal lens with a thinner liquid crystal lens (385) and a thicker liquid crystal lens (365) separated by a single shared electrode (370). Wherein the thinner liquid crystal lens (385) has a smaller optical power and a faster response time and the thicker liquid crystal lens (365) has a larger optical power and a slower response time. The autofocus system has a focusing effect that is produced by the combined optical power of the thinner liquid crystal lens and the thicker liquid crystal lens. A method for focusing an image capture device and an image capture device are also described.

Abstract: Apparatus for concentrating light rays arriving from at least one opening onto a receiver, individual beams of the light rays each arriving at the apparatus substantially collimated, the apparatus including a respective Fresnel lens assembly for each opening, the Fresnel lens assembly including a first Fresnel lens, and a second Fresnel lens, the first Fresnel lens being located between the opening and the receiver, the second Fresnel lens being located between the first Fresnel lens and the receiver, the first Fresnel lens collimating the light rays arriving from the opening, the second Fresnel lens converging the collimated light rays onto the receiver, the opening being located in front of the Fresnel lens assembly, on the focal plane of the first Fresnel lens, centered on the focal point of the first Fresnel lens, and the receiver being located behind the Fresnel lens assembly, on the focal point of the second Fresnel lens.

Abstract: To provide a Fresnel lens wherein changes in focal length due to temperature dependence of the refractive index can be compensated. By introducing a fractal structure into prisms in a peripheral region in which the prism angle is large and therefore the aspect ratio h/p of the prisms is large, the aspect ratio is reduced from h/p to h?/p and the slope of the envelope 20 to the underside of the slopping face is reduced, and thereby a shape in which a change in focal length due to temperature dependence of refractive index can be compensated for by a change in the shape of lenses due to expansion/contraction, is obtained.

Abstract: A variable focus lens system that can be used in eyeglasses is disclosed. The system consists of superimposed first and second transparent thin lenses with surfaces divided into Fresnel zones and zone boundaries. The lenses are relatively slidable for focus adjustment. The Fresnel zone boundary surfaces are made parallel to the user's optical line of sight to reduce visual obstructions, and the zone boundaries may be restricted to areas near the lens periphery to further reduce visual obstructions. An opaque light absorbing coating may be applied to the zone boundaries to reduce light scattering. A fixed prescription lens, having the user's distance and astigmatism corrections, may be superimposed on the other two lenses.

Abstract: A exemplary light converging device includes a support, a supporting plate, a reflective Fresnel lens and a cooling assembly. The supporting plate is rotatably mounted on the support. The reflective Fresnel lens is fixedly mounted on the supporting plate. The cooling assembly is positioned between the reflective Fresnel lens and the supporting plate. The cooling assembly is thermally coupled to the reflective Fresnel lens and configured for cooling the reflective Fresnel lens.

Abstract: A composite optical device 1 includes a first optical section 10 having an optical functional surface 11 and a second optical section 20 bonded to the first optical section 10 on the optical functional surface 11. The optical functional surface 11 includes a smooth part 13 and a concave-convex part 12 adjacent to each other, and is constructed so that a position P2, along a normal direction of the smooth part 13, of a concave bottom of the concave-convex part 12 can be closer to the center of the first optical section 10 than a position P1 along the normal direction of an end of the smooth part 13 on a side of the concave-convex part 12 in a boundary vicinity portion NR between the smooth part 13 and the concave-convex part 12.

Abstract: An optical device directs light from a light source to a region of space, such as the field of view of a camera when the optical device is used as a camera flash unit. This device includes a first optical element which converges light from the light source towards an inner portion of the region to be illuminated and a second optical element which diverges part of the light from the first element outwardly towards an outer portion of the region to be illuminated so as to achieve adequate central illumination with improved uniformity of illumination across the region to be illuminated. The second optical element may have a concave multiple-faceted surface comprising plane facets in the shape of an open-base inverted truncated pyramid, contiguous sector-shaped facets, at least some of which are concave, or a face divided into an elongate portion disposed between first and second diverging portions.

Abstract: A direct-viewing type display device according to the present invention includes: at least one display panel having a display region and a frame region formed outside of the display region; and at least one Fresnel lens plate disposed on a viewer side of the at least one display panel with a predetermined interval therefrom. The Fresnel lens plate includes a Fresnel lens region at a position overlapping a region that contains a portion of the frame region of the display panel and a portion of a peripheral display region within the display region that adjoins the portion of the frame region along a first axis. A portion of display light exiting the portion of the peripheral display region is emitted from a region of the Fresnel lens region that overlaps a portion of the frame region, or a region outside the region, toward the viewer side.

Abstract: A light receiver comprises a Fresnel lens for collecting light signals, and a light receiving element disposed closer to the Fresnel lens than the focal point of the Fresnel lens for receiving the light signals collected by the Fresnel lens. The Fresnel lens comprises a lens surface group having a plurality of lens surfaces, and a back cut surface group having a plurality of back cut surfaces connecting the lens surfaces. The back cut surfaces are inclined with respect to the center axis of the Fresnel lens. Thus, the light receiver has a high light collection efficiency of light signals incident within a certain acceptance angle.

Abstract: An exemplary Fresnel lens includes a flat emitting surface and a plurality of annular Fresnel lens elements at an opposite side thereof to the emitting surface. Each of the Fresnel lens elements has a non-lens surface perpendicular to the emitting surface and a Fresnel lens surface adjoining the non-lens surface with an acute angle. Each of the Fresnel lens elements has a plurality of spaced cavities defined in the non-lens surface.

Abstract: A lens device includes a base, groups of prism-like elements formed on the base and at least two alignment points formed on the base. Each of the groups and a related portion of the base form a lens. Each of the prism-like elements comprises an incidence surface in the form of a camber. The alignment points are used for alignment of a laser device with the lens device.

Abstract: A convex-Fresnel LED lens and a LED assembly thereof are revealed. The lens is a Fresnel lens whose optical surface on a forward side thereof is a convex surface having draft with vertical shape so that the lens in the LED assembly concentrates light emitted from a LED chip to generate light whose peak intensity is an elliptic distribution pattern. Moreover, the lens and the LED assembly thereof satisfy certain conditions. Thereby, light from the LED chip is gathered by a single lens to form a preset specific distribution pattern and is satisfying requirement of the ratio of the luminous flux that is larger than 85%. The convex-Fresnel LED lens and a LED assembly thereof are applied to lights and flashlights in mobile phones or cameras.

Abstract: A display apparatus is provided. The display apparatus includes a front side that is exposed the outside. A refractor or set of refractors is positioned so as to minimize the appearance of a shield member to a viewer, thus causing a non-display region of the display apparatus to appear to be smaller than its actual size, thus increasing a size of an image display region of the display apparatus.

Abstract: A display apparatus is provided. The display apparatus includes a front side that is exposed the outside. A refractor or set of refractors is positioned so as to minimize the appearance of a shield member to a viewer, thus causing a non-display region of the display apparatus to appear to be smaller than its actual size, thus increasing a size of an image display region of the display apparatus.

Abstract: A display apparatus is provided. The display apparatus includes a front side that is exposed the outside. A refractor or set of refractors is positioned so as to minimize the appearance of a shield member to a viewer, thus causing a non-display region of the display apparatus to appear to be smaller than its actual size, thus increasing a size of an image display region of the display apparatus.

Abstract: A light emitting diode (10) includes an LED chip (14) and an encapsulant (16) enclosing the LED chip. The LED chip has a light emitting surface (141), and the encapsulant has a light output surface (161) over the light emitting surface. The light output surface defines a plurality of annular, concentric grooves (163). Each groove is cooperatively enclosed by a first groove wall (165) and a second groove wall (166). The first groove wall is a portion of a circumferential side surface of a cone, and a conical tip of the cone is located on the light emitting surface of the LED chip.

Abstract: A Fresnel lens includes a plate made of a glass material and Fresnel portions made of plastic material and integrally formed onto the plate. A method of manufacturing the Fresnel lens includes the steps of adding the plastic material in a forming apparatus, curing the plastic material, and then separating the forming apparatus and the plate from each other to form the Fresnel lens. An apparatus for manufacturing the Fresnel lens includes a forming apparatus coupling with the plate of the Fresnel lens, and a forming concave with inversion corresponding to the shape of the forming Fresnel portions. The forming concave shapes the plastic material into the Fresnel portion. Therefore, the Fresnel lens takes lower manufacture cost than the glass Fresnel lens and has better reliability than the plastic Fresnel lens while exposing in high temperature and high light density.

Abstract: There is disclosed a perfectly plain FRESNEL zone lens. The perfectly plain FRESNEL zone lens includes a plurality of focusing units and a grid formed together with the focusing units by injection molding for example. The grid consists a plurality of cells. Each of the focusing units is disposed in a related one of the cells.

Abstract: The invention concerns a security document (7) having a first transparent region (72) in which a first transparent optical element (74) is arranged and a second region (71) in which a second opaque optical element (73) is arranged. The second opaque optical element (73) exhibits a first optical effect. The first region (72) and the second region (71) are arranged in mutually spaced relationship on a carrier (75) of the security document, in such a way that the first and second regions can be brought into mutually overlapping relationship. Upon overlap of the second optical element with the first optical element with a first spacing (26) between the first and second optical elements a second optical effect appears and upon overlap of the second optical element with the first optical element with a second spacing (25) between the first and second optical elements, which is greater than the first spacing (26), a third optical effect (51) which is different from the second optical effect appears.

Abstract: A surface of a base material of a Fresnel lens has a central area having circular zones arranged therein and an outer area located on the outer side of the central area and having circular-arc zones arranged therein. The pitch of zones in a boundary area between the central area and the outer area and where the zone shape changes is smaller than a basic pitch which is the pitch of the circular and circular-arc zones in the central area and the outer area.

Abstract: A device for shaping laser radiation, in particular for laser radiation emitted by a laser diode bar, has at least one substrate with a plurality of refractive boundary surfaces through which the laser radiation to be produced can pass in such a way that at least two partial beams of the laser radiation, which, prior to their passage, are adjacently arranged in a first direction, are adjacently arranged after their passage through the refractive boundary surfaces in a second direction which is perpendicular to the first direction. The refractive boundary surfaces are formed at a substrate or at substrates that are connected to one another.

Abstract: Each of a plurality of Fresnel prisms 12 is formed so that a refractive surface 12 thereof includes a non-light incidence surface 12c upon which any light ray emitted from a projector 1 is not directly incident because it is intercepted by another Fresnel prism 12, the non-light incidence surface having an angle ?? with a reflective surface 12b which is different from the prism apex angle ? of each of the plurality of Fresnel prisms. As a result, a light ray reflected by the refractive surface 12a of each of the plurality of Fresnel prisms without passing through the refractive surface can be preventing from emerging, as unnecessary light, toward the viewer's line of sight.

Abstract: A plurality of first refraction surfaces 121 and a plurality of second refraction surfaces 122 are alternately provided on an emission surface of a lens element 120 so as to form concentric circles each having an optical axis 113 at the center thereof, and having diameters different from each other, and a light reflected by a plurality of reflection surfaces 123 provided on an incident surface of the lens element so as to form concentric circuits each having the optical axis 113 at the center thereof and having diameters different from each other, is refracted and emitted by the plurality of second refraction surfaces 122 at desired angles. Therefore, it is possible to enhance efficiency and an emission intensity, and reduce variations in brightness of an emitted light without increasing the diameter of the lens element 120, thereby realizing a light emitting module 100 enabling advantageous performance.

Abstract: There are provided an objective lens for an optical pickup device which can record and/or reproduce information on/from an optical disk with high density with the use of a light flux with a short wavelength while keeping a temperature characteristic to be satisfactory in spite of having a plastic objective lens, and the optical pickup device. The objective lens suppresses generation of a spherical aberration even if a temperature change arises, by sacrificing wavelength characteristics and by enhancing temperature characteristics. Such satisfactory temperature characteristics can be acquired by the ring-shaped structure formed as a turning structure on an optical surface of the objective lens, in which the ring-shaped structure includes ring-shaped zones whose number is 3 or more and 30 or less and the ring-shaped structure is formed such that adjoining ring-shaped zones cause a predetermined optical path difference for an incident light flux.

Abstract: Various embodiments of a rear-projection screen, a method of rear-projection collimation and a projection video display (PVD) system. In one embodiment, a rear-projection screen includes: (1) a total-internal-reflection (TIR) fresnel lens configured to aim light received at an incidence angle toward a central axis of the TIR fresnel lens at a convergence angle and (2) a refractive fresnel lens configured to refract the light received from the TIR fresnel lens and at least to reduce the convergence angle.

Abstract: A method for laminating a film on to an optical article and a bi-layer adhesive for use in the method. The bi-layer adhesive includes a latex adhesive layer and an HMA layer sequentially disposed on the film and dried to form a solid layer of uniform thinness throughout to provide optical quality. Various types of films may be employed to provide an optical function. Following optional pre-treatment steps, the adhesives are coated on to the film. An optical hot press technique is used to deliver heat and pressure over a short period of time to form a functionally-enhanced optical article with high adhesive strength.

Abstract: When using an acrylic resin with a refractive index of 1.494, for example, the structure of the Fresnel lens is such that in a segment where a deviation angle of 19.5° or less is required, refraction-only prisms which do not cause any reflections are used, while in a segment where a deviation angle of 31.0° or larger is required, single-step total reflection prisms in which light is totally internally reflected once and then refracted are used and, in a segment where a deviation angle not smaller than 19.5° but not larger than 31.0° is required, two-step total reflection prisms in which light is totally internally reflected twice and then refracted are used.