Multiplexing Prisms for Field Expansion

Abstract

Purpose: Prisms used for field expansion are limited by the optical scotoma at a prism apex (apical scotoma). For a patient with two functioning eyes, fitting prisms unilaterally allows the other eye to compensate for the apical scotoma. A monocular patient's field loss cannot be expanded with a conventional or Fresnel prism because of the apical scotoma. A newly invented optical device, the multiplexing prism (MxP), was developed to overcome the apical scotoma limitation in monocular field expansion.

Methods: A Fresnel-prism-like device with alternating prism and flat elements superimposes shifted and see-through views, thus creating the (monocular) visual confusion required for field expansion and eliminating the apical scotoma. Several implementations are demonstrated and preliminarily evaluated for different monocular conditions with visual field loss. The field expansion of the MxP is compared with the effect of conventional prisms using calculated and measured perimetry.

Results: Field expansion without apical scotomas is shown to be effective for monocular patients with hemianopia or constricted peripheral field. The MxPs are shown to increase the nasal field for a patient with only one eye and for patients with bitemporal hemianopia. The MxPs placed at the far temporal field are shown to expand the normal visual field. The ability to control the contrast ratio between the two images is verified.

Conclusions: A novel optical device is demonstrated to have the potential for field expansion technology in a variety of conditions. The devices may be inexpensive and can be constructed in a cosmetically acceptable format.

Figures

Figure A1

Contrast reduction of the target in the shifted view of a 57Δ MxP with various aperture ratios ( r= 40%, 50%, and 60%). Due to the variation of the transmittance in the prism elements and fixed transmittance in the flat elements, the contrast reduction in the MxP is controlled by the transmittance variations in the prism elements. In the EPS configuration, the contrast is almost the same as the aperture ratio, though it drops close to zero near TIR in higher eccentricities. In the OPS configuration, however, the wide variation in transmittance with gaze angle results in highly reduced contrast, especially when approaching the critical angle of incidence.

Figure 1

Multiplexing prisms (MxP). (A) Schematic profile of a conventional Fresnel prism segment showing the light deviating towards the base in each element. Profile of a multiplexing prism segment alternating the flat and prism elements in (B) flat-bottom type and (C) flat-top type. The prism elements deflect rays and shift the view via prismatic effect (blue dashed lines), while the see-through view passes through the flat elements (red dotted lines). The user can see multiplexed (superimposed) see-through and shifted views.

Figure 2

Prototypes of the multiplexing prisms. (A) Micrograph of a molded mostly flat-bottom type prototype (with small flat top elements as well) 40Δ MxP with equal aperture ratio (B) Micrograph of 57Δ flat-top type MxP with equal aperture ratio manufactured by grinding and polishing a Fresnel prism.

Figure 3

Multiplexing prism glasses for a monocular patient (left eye only) with left hemianopic field loss. (A) Calculated Goldmann perimetry diagram for the primary gaze field of view of the patient fitted with upper and lower base-left 30Δ horizontal peripheral prisms. The expanded view into the left blind hemifield comes with the loss of right side view due to the apical scotomas. (B) Ray diagram (viewed from above) for the configuration shown in (A), illustrating the shifted view and source of the apical scotomas. (C) Calculated Goldmann perimetry diagram of the same monocular patient when MxPs are used. There is true field expansion with no field lost to apical scotomas. (D) The corresponding ray diagram shows shifted (red dashed lines) and see-through (blue solid lines) views falling on the same retinal area with visual confusion.

Figure 4

Variation of deflection power (in degrees) and transmittance of the prism elements in 57Δ PMMA MxP (39° apex angle with n = 1.49). A negative sign indicates an angle toward the base side of the prism. (A) The prism deflection power (proportional to field of view expansion) varies with the angle of incidence much more in the outward prism serrations (OPS) configuration. Due to total internal reflection (blue dotted arrows), the OPS prism cannot deflect light beyond the −5.3° critical angle of incidence. In the eyeward prism serrations (EPS) configuration, the angle of incidence is reduced, which reduces the prism deflection power. However, the reduction avoids total internal reflection and provides more constant prism power over the practical eye scanning range (±15°). total internal reflection is eventually encountered at about −44° (red dotted arrows). (B) The transmittance in the flat elements of the MxP is constant at 92% (and starts to drop at about 50° eccentricity) and the EPS prism elements have almost the same transmittance within the practical eye scanning range. In both configurations, the transmittance varies with the angle of incidence and reduces sharply when approaching the critical angle of incidence, which in the OPS configuration is well within the eye scanning range, while in the EPS configuration it is at the far limit of eye scanning.

Figure 5

Photographs of the views through conventional Fresnel and multiplexing prisms with the prism in OPS and EPS configurations (base-left 57Δ flat-top MxP with 50% aperture ratio). The camera exposure and aperture settings were fixed so that the contrast differences can be compared among the various conditions. (A) An image of the savannah cartoon (Fig. 1A in Apfelbaum & Peli) without the prisms. Blue rectangle indicates the portion of the scene within the see-through view, spanning 48° horizontally. Red dotted and dashed rectangles outline the portion of the scene within the shifted view in the OPS and EPS configurations, respectively. (B) Photo through a conventional OPS Fresnel prism shows a right shifted view with minification (horizontally compressed tiger and highly compressed rhinoceros at the red arrows). Dimming of the shifted view left of the rhinoceros due to total internal reflection results in only the spurious reflections from the right being seen. Note mirror reversal reflections of objects in this area. (C) Conventional EPS Fresnel prism shows less shifted view. The rhinoceros and the tiger in (B) are farther to the right than in (C), with magnification on the right (see the magnified lion) and there is no total internal reflection (within the range seen). Weak spurious reflections are everywhere (but more visible on the left; see the horizontally flipped elliptical pool and grass blades). (D) OPS MxP shows both shifted and see-through views. Note the doubled sun and animals. The contrast of both views is reduced to 50% by the aperture ratio. The transmittance reduction of the shifted view around the area of total internal reflection results in lower contrast (see a much fainter tiger in the cage). In the total internal reflection range, the shifted view is dimmed. As a result, the see-through view is seen with higher contrast (higher contrast lion, giraffe, and tiger). In addition, the spurious reflections in the total internal reflection area are suppressed by the see-through luminance. (E) EPS MxP shows both the shifted and see-through views (doubled animals). On the right (apex side), the slightly reduced transmittance of the shifted view lowers its contrast (lion). In other areas, the contrast is higher and equal in both shifted and see-through views (50% aperture ratio). The spurious reflections across the visual field are low contrast and hardly visible.

Figure 6

Field expansion for a monocular patient with left (incomplete) hemianopic field loss. (A) Goldmann perimetry without prisms showing a residual field in the lower left quadrant. The red dotted lines indicate the presumed fitting position of the prisms (note the prism position relative to the field varies with head posture). (B) Goldmann perimetry (field of view) with conventional OPS peripheral prisms (57Δ, base left), showing field substitution with apical scotomas. Expansion of the lower field is about the same as the upper field, despite the lower residual field, because of the field of view limitation imposed by total internal reflection (left 5°). (C) With OPS MxPs (57Δ), the apical scotomas are eliminated, providing true field of view expansion. The dashed line on each plot represents the boundary of the seeing field without prisms. The scotoma at the horizontal meridian to the right of the fovea is the patient’s enlarged physiological blind spot.

Figure 7

Field of view expansion glasses (57Δ) for a monocular patient (left eye blind) with severe peripheral field loss. (A) MxP spectacles provide scotoma-free views from the left (base-in upper prism) and right (base-out lower prism) field. For a patient with 20° diameter residual central field, the prisms are separated vertically by 3.5mm (~10° of visual angle), affecting the upper and lower 5° of the residual field. The shifted partial iris and eyelid views (seen in the upper and lower prisms) are superimposed on the eye’s see-through view. Calculated perimetry for (B), the effect of conventional Fresnel prism glasses, and (C), the MxP spectacles shown in (A) with OPS MxPs, illustrates the benefit of MxPs. While the conventional Fresnel prisms just substitute fields due to the apical scotoma (split residual central field), the narrow central field is expanded to both sides by the MxPs. The peripheral islands are wider than the residual field they are imaged upon due to the minification effect in the OPS configuration.

Figure 8

Field of view expansion of a monocular (right eye) patient with peripheral field loss and poor visual acuity (20/500). (A) PC-based perimetry without the prism. The red dotted outline represents the presumed prism position. The actual prism position varies with head posture. (B) Field of view with an EPS Press-On prism (40Δ). The field is shifted as well as the accompanying apical scotoma. Due to the upper prism position that covers the upper boundary of the visual field, the apical scotoma is connected all the way to the upper boundary of the visual field. (C) With an MxP in EPS, the apical scotoma is eliminated and there is true field expansion, not a just substitution. Black dashed line on each plot represents the boundary of the seeing field without prisms.

Figure 9

Binocular perimetry for a patient with severe field loss due to retinitis pigmentosa, wearing upper MxPs 40Δ base out on each carrier lens. There are two expansion areas (seen monocularly) and no apical scotomas. The left eye prism, base left, was tilted obliquely down bringing the expansion area on that side closer to the horizontal midline.

Figure 10

MxP glasses for a monocular patient with a blind left eye. (A) Wraparound sunglasses with a 40Δ EPS conventional Press-On prism mounted over the bridge. The left extent of the prism could be much shorter than used here, but is inconsequential as it is in front of the blind eye. (B) Field substitution and an apical scotoma of 20º result with this conventional prism design. The unaided monocular field is shown within the dashed line. (C) Wraparound sunglasses with a 40Δ EPS MxP attached. (D) Field expansion without an apical scotoma is achieved with the prototype MxP in the same position. Lower contrast and visual confusion due to the multiplexing is expected but not shown here. The edges of the prism in (A) were highlighted in black to improve the visibility of the illustration.

Figure 11

Expanding the normal peripheral field. (A) A conventional PMMA 40Δ OPS Fresnel prism mounted base out on the lateral wing of a pair of safety glasses. (B) The field measured with the spectacles shown in (A). The subject was facing and fixating 90º from the center of the perimetry screen. The thick solid line illustrates the area covered by the perimetry screen, as projected on a Goldmann like polar graph. An expansion of about 10° with a corresponding apical scotoma of similar size was measured. The normal field, measured without the prisms, is indicated by the dashed line. (C) A segment of MxP OPS 40Δ is placed at the same position on the spectacles. (D) The field recorded with the MxP shows absence of any apical scotoma. The shorter (vertically) expanded area is due to the narrower prism segment used in this case.

Figure 12

Mean measured contrast reduction factors for 40%, 54%, and 68% ratios of EPS MxPs (14% step of aperture ratio among samples) with 7 normal subjects. The measured contrast reduction factors are proportional to the aperture ratio though they are little lower than the calculated reduction factor. Note that each measured factor is 11%, 13%, and 14% smaller than the aperture ratio (40%, 54%, and 68%, respectively). Error bars represent the standard error of the mean.