An optical see-through head-mounted display (OST-HMD) can optically superimpose computer-generated virtual scenes onto the views of a real-world scene in mixed or augmented reality systems [1]. Rather than a video see-through approach, the OST-HMD has an actual direct view of the space in front of the user, which introduces minimal degradation to real-world scenes. The OST-HMDs are widely employed in the fields of medicine [2], manufacturing [3], scientific visualization [4], aviation [5], education, and entertainment [6].

However, it is difficult to achieve a large field of view (FOV), low F/#, compact, and nonintrusive OST-HMD through a nonpupil-forming system [1]. Optical designers have tried various optical solutions for such problems, including, but not limited to, catadioptric systems, geometric waveguides, diffraction waveguides, freeform prisms, light fields, and metasurfaces. Each of these technologies has a unique disadvantage. For example, although a catadioptric lens system can avoid the effects of stray light and ghost images, achieving a compact form may deem quite challenging [7]. Similarly, the optical distortion of the projected image is difficult to correct during the design process [8–10]. The OST-HMD integrating the projection optics and waveguide easily meets the requirements of small thickness and light weight. However, the stray light of the geometrical waveguide severely degrades the display quality when high processing technology is required [11–14]. For diffraction waveguides, it is still difficult to develop full-color, high-resolution displays that are free of artifacts such as speckles [15–20]. Improvements in design and manufacturing ability have made freeform optics broadly applied to imaging systems [21–25]. The performance of the freeform prism OST-HMD has progressed significantly. Thus, a wide FOV and low F/# OST-HMD can be achieved using a freeform prism while maintaining compactness and light weight, but large distortion and anamorphic ratio remain [26–28]. A light-field near-eye display can obtain a corrected depth perception of the virtual information in OST-HMD applications. Transparent display panels are rare and have low resolution, which cannot be achieved in a short time [29,30]. Metasurfaces have shown remarkable potential for manipulating light in imaging systems [31–36]. Metalens, produced only by nanoimprinting, can overcome the existing bottleneck imposed by the narrow FOV and bulkiness of the current systems. The limitation of processing methods is their inability to be widely promoted [37].

OST-HMD system structures are classified into four types: general catadioptric system, diffractive waveguide, geometrical waveguide, and freeform prism. Table 1 lists the module views, pros, and cons of these four solutions as well as commercially available HMD products based on these solutions, such as ODG R-9 [38], Magic Leap 1 [39], Lumus DK-52 [40], and our previous design in Ref. [26].Table 1.

Comparison of Four OST-HMD Optical Solutions

The development of freeform surface description and design methods has promoted a revolutionary leap for the advancement of the OST-HMD technology. Although the freeform element is thicker than waveguides, plastic material has much less specific gravity and keeps its weight. Its fundamental difference from waveguides is that light efficiency of freeform prisms is no longer restricted by diffraction efficiency or reflectance of reflective mirrors, so its light efficiency is higher than those of waveguides and general catadioptric systems. That is why the waveguide OST-HMD system needs a Pico projection system, and the overall thickness of the waveguide system is similar to or even larger than that of the freeform optics solution. Briefly, the freeform prism is an advantageous modern solution to achieve OST-HMD designs with better display performance.

In this paper, we present the design of an OST-HMD system that includes three wedge-shaped freeform prisms and two lenses. Using a 0.71-in. (1 in. = 2.54 cm) microdisplay, the system offers a diagonal FOV of 45.3°, an F/# of 1.8, an eye relief of 18 mm, an exit pupil diameter as large as 12mm×8mm, and vision correction capability. The distortion of the virtual image light path and the see-through light path is only 0.6% and 0.4%, respectively, indicating that the distortion is well controlled. The rest of the paper is organized as follows. In Section 2, we review and compare previous research using freeform prisms in HMD designs. In Sections 3–6, we describe the display principle and system specifications of our design, design of the virtual image light path, system optimization methods, and prototype testing results.

The concept and development of freeform prisms have been elaborated in previous studies [26]. Freeform prisms have shown significant advantages in the design of compact HMD systems. The wedge-shaped freeform prism provides full play to the characteristics of the total internal reflection and minimizes light loss. The correcting plate effectively corrects the see-through light path, reduces deformation of the external scene, and achieves high-quality virtual and real registration. After extensive research, the freeform prism has been applied to current OST-HMD systems and has been commercially available. Many companies, such as Olympus [41], eMagin [42], and Rockwell Collins [43], have released HMDs or optical modules based on freeform prisms.

In our previous research paper [26], we designed an OST-HMD based on a freeform prism. Along with the deep development of the study, different types of freeform prism OST-HMDs have been commercially available [44]. However, the shortcomings of the design in Ref. [26] still intervene with the wearable experience. For example, if the distortion of the virtual image light path is up to 12%, electronic correction is required when this optical system is applied in OST-HMD applications. Although the see-through distortion is only 1.4%, the design process of the auxiliary prism is complicated and difficult, and the image quality of the real scene decreases. Diopter adjustment is also an important function for OST-HMDs. Previous designs cannot achieve diopter adjustment, causing some users to wear two pairs of glasses.

To address the problem of see-through distortion of freeform prism OST-HMD, an auxiliary lens was added between the main wedge-shape prism and the eye [45]. This auxiliary lens can also achieve the diopter adjustment function [46,47]. In Table 2, we list the optical path evolution process. In this paper, we compare our previous design, the three-piece prism design [45], and our present design across all aspects.Table 2.

Specifications of Different Freeform Prisms

The current solution entails that the distortion of the virtual image light path is less than 0.6% without electronic correction, projecting a clear and undistorted image from the microdisplay to the user’s eye. In addition, a larger exit pupil diameter is achieved in this new design, thereby simplifying the structure by avoiding the pupil adjustment mechanism. Due to the addition of the auxiliary lens, which makes the optical surface near the human eyes flat or spherical, it is much easier to design the see-through light path in the present design. In addition, we achieve diopter adjustment by changing the shape of the first surface of the auxiliary lens to meet the diopter needs of different users, while other optical elements remain unchanged. This process is described in Section 4.B. Although the FOV of the present design is slightly smaller than that of our previous design, it is similar to other optical solution types and is still able to meet the usage requirements of AR applications.

An optical see-through HMD typically consists of an optical path for viewing a displayed virtual image and a path for viewing a real-world scene directly. The previous design included only two freeform elements: a main prism and a correct plate. Although it had a larger FOV, lighter weight, and simpler structure, it retained unsolvable defects, as mentioned in Section 2. Therefore, it is necessary to improve the performance of previous designs. The OST-HMD optical system presented in this study is shown in Fig. 1. The overall system is set to be symmetric about the YOZ plane, comprising three freeform prisms and two rotationally symmetric lenses.

In the present design, two extra lenses close to the microdisplay are used to improve the image quality of the system, balancing the performance across the entire exit pupil. The wedge-shaped freeform main prism E2 assumes the larger part of the optical power, magnifying the image from the microdisplay. The 1st auxiliary lens is placed between the main prism E2 and human eye and is effective in correcting the distortion of the system, just as it is necessary to achieve the diopter adjustment function. In addition, the 1st auxiliary lens E1 is conducive to counteracting the optical path difference of rays of different fields caused by the off-axis setup. On the right side of E2, the 2nd auxiliary lens E5 is cemented with E2, completely correcting the see-through distortion.

As shown in Fig. 1, the wedge-shaped freeform prism E2 and the 1st auxiliary freeform element E1 consist of three and two optical effective surfaces, respectively. The 2nd auxiliary freeform element is similar with E1. The system is optimized with rays traced from the exit pupil to the microdisplay, the optically effective surfaces are denoted by S1 and S2 of E1, S3−S5 of E2, S6−S10 of E4 and E5 for virtual image path. Surfaces S4′ and S10 with S1−S4 are for the see-through light path. Surfaces S2−S5 are freeform surfaces, while others are spherical or have a flat surface.

For the elements in the optical system, the main prism and 1st auxiliary freeform element are adjacently arranged. The surface S2 of E1, is proximate to the surface, S3, of the main prism E2, and there is a small air gap between them for total internal reflection condition. Surface S4′ of the 2nd auxiliary freeform element E5 has the same surface shape as S4 of the main prism E2 to ensure that the E5 and E2 would be perfectly cemented. Surface S10 of the E5 should be parallel to the surface S1 of E1, no matter with or without requirement of diopter accommodation.

The virtual image light path consists of the 1st auxiliary freeform element E1, the main wedge-shaped prism E2, two lenses E4 and E5, and the microdisplay. The light emitted from the microdisplay is first transmitted through lenses E4 and E3, and refracted into the main prism E2 by the surface, S5, close to the lenses. After two consecutive reflections on surfaces S3 and S4 in the main prism, it reaches surface S3 for the second time. Then, light is transmitted out of the surface S3 of the main prism into the air gap between the prism E2 and auxiliary freeform lens E1 and enters E1 by surface S2. Finally, light is projected through surface S1 to the exit pupil, entering the human eye.

Some transmission light is lost during the first reflection on surface S4 to reduce the power of the microdisplay. To prevent such light from entering human eyes, it is necessary to always have the light reflected by the surface, S3, satisfying the total internal reflection (TIR) condition. Therefore, only if there is an air gap between the surfaces S3 and S2, light travels in the direction from a medium with a higher refractive index to a medium with a lower refractive index so that total internal reflection is possible.

For the see-through light path, light from the real-world scene enters surface S10 of the correcting plate and transmits through surface S4′, which is cemented with surface S4 of the main prism, into the main prism. In addition to the light from the microdisplay, the light transmits through the body of the main prism, into the air gap, and then through the auxiliary lens E1, finally exiting from the surface, S1, and entering the human eye.

Surface S4 of the main prism was coated with a beam-splitting film. Consequently, the rays from the microdisplay are partially reflected by surface S4, similar to the rays from the real-world scene.

In the previous design [26], the surface close to the eyes is a freeform surface, causing viewing axis deviation, undesirable distortion, and other off-axis aberrations in the view of the real-world scene. Although the correcting plate corrected the deviation of the optical axis and the off-axis aberrations introduced by the freeform prism, there is still approximately 1.4% distortion of the see-through light path. The design of the correcting plate was complicated. However, in the present design, the surface close to the eyes is flat or spherical, which simplifies the design process of the see-through light path and reduces the distortion. In addition, the 1st auxiliary lens E1 is an essential element for achieving the diopter adjustment function. For the virtual image light path, we change the shape of surface S1 to adjust the virtual image distance. Hence, people with blurred vision can see a virtual image without wearing two pairs of glasses. For the light path, the curvature difference between surface S1 and surface S10 can be matched to adapt to the user’s diopter. To achieve the diopter adjustment function, a series of auxiliary lenses with different shape of surface S1 should be produced, and customization is available to users with different diopters.

The overall specifications of the system are listed in Table 3. Based on various considerations of volume, resolution, availability, and cost, a 0.71-in. organic LED (OLED) display with a resolution of 1920×1080pixels and an 8.2 μm pixel size is selected. In the design of visual instruments, especially binocular HMDs, a large exit pupil diameter (EPD) is essential to prevent vignetting or loss of image due to the rotation of the eyes. A large EPD is highly adaptable to the interpupillary distances among different users and avoids mechanically adjusting the interval of the binocular optics. However, a large EPD will affect the compactness, weight, and FOV of the optical system, resulting in a sharp increase in the challenge of designing low F/# systems. Considering these factors, we set the exit pupil diameter to be 12mm×8mm and the focal length to be 21.6 mm, resulting in an F/# of 1.8. Then, a 45.3° diagonal full FOV was determined. Although the FOV is smaller than that of our previous design [26], a larger EPD provides a better wearable experience.Table 3.

Overall Parameter Requirements of the System

In a freeform optical system, the distortion can be quite large and irregular if there are no constraints. Therefore, we need to control the imaging distortion to less than 0.6% to avoid electronic correction of the initial image source. Compared with other evaluation methods of image quality, the modulation transfer function (MTF) is more suitable for evaluating the overall image sharpness. The MTF value would be better than 40% at a spatial frequency of 50 lp/mm in the full FOV.

The additional use of the 1st auxiliary freeform lens E1 makes the design of the see-through light path very easy; this section just needs to discuss the design of the virtual image light path. Optical freeform surfaces exhibit nonrotational symmetry. In most cases, an optical system with freeform surfaces can obtain higher image quality. In contrast to traditional optical surfaces, such as spherical or aspherical surfaces, several surface description methods of freeform surfaces can be used in the design of nonrotationally symmetric optical systems. The variety of freeform surface expressions provides more flexibility during the process of designing a freeform surface optical system. We have described, in detail, the type of freeform surface representation, strategy of freeform surface design, and method of maintaining the TIR condition in previous papers [26]. Therefore, this section focuses on structural constraints in the process of designing an OST-HMD and diopter adjustment based on the 1st auxiliary freeform lens E1 and wedge-shaped freeform prism E2.

To guarantee that the rays of all fields pass through the optical system correctly and enter the user’s eyes, it is essential to control the structure of the main freeform prism, make its three surfaces form a valid prism shape, and ensure that the center and edge thicknesses meet the manufacturing requirements. The methods to optimize the physical structure of the wedge-shaped freeform prism are as follows.

By controlling the position relations of specific points and lines, we can constrain the structure of the main prism. Figure 2 illustrates the structural control method employed in this study. Two reference rays are selected to follow the constraints in the optimization process: the upper marginal ray, R1, of the maximum field in the positive Y direction, and the lower marginal ray, R2′, of the maximum field in the negative Y direction. As shown in Fig. 2, Pa0, Pa1, Pa2, and Pa3 denote the intersection points of the ray R2′ with surfaces S3, S4, and S5, respectively; Pb0, Pb1, and Pb2 denote the intersection points of ray R1 with surfaces S3, S4, and S5, respectively; and Pc0 represents the intersection point of the chief ray with surface S5.

By constraining the points Pa1 and Pb0 locating down the line Y1, a segment Pa2Pa3 of lower marginal ray R2′, we ensure that surfaces S3 and S4 intersect properly so that both the upper marginal ray and the lower marginal ray can be traced through the prism without obstruction. In a similar manner, the points Pa3 and Pb2 must be constrained above the line Y2, a segment Pb0Pb1 of upper marginal ray R1. Consequently, the surface S5 will, respectively, intersect the surfaces S4 and S3 correctly, avoiding the escape of the upper marginal ray and controlling the thickness of the prisms.

Commercial optical design and analysis software CODE V [48] develops a physical structure control function, referred to as JMRCC, which can be used to define the aforementioned constraints easily. This function computes the signed perpendicular distance from a point to a line in the YZ plane. It can, thus, create clearance or interference constraints when optimizing off-axis reflective/catadioptric systems. The input parameters of the JMRCC function are a single ray and a single point. The distance between the point and line is the output. Considering the mathematical and geometric rules, the output value should be positive when the point locates above the line; otherwise, the output value should be negative. As shown in Fig. 3, the JMRCC function builds a constraint about the distance between line L and point P, which can be expressed as D=JMRCC(L,P).(1)

According to the above discussion, the constraints to maintain the physical structure of the main prism can be given as follows: {JMRCC(L1,Pa1)≤−0.1JMRCC(L1,Pb0)≤−0.1JMRCC(L2,Pb2)≥0.1JMRCC(L2,Pa3)≥0.1.(2)

Similarly, we can construct specific constraints and use the JMRCC function to effectively ensure the shape of all prisms logically.

For most OST-HMD systems, devices did not include diopter adjustment. Users with myopia or hyperopia were required to wear two pairs of glasses simultaneously. Some devices attained diopter adaption by placing an additional corrective lens between the human eye and OST-HMD, as shown in Fig. 4(a), but such deemed tedious for users to fit it [46]. Meanwhile, the corrective lens complicates the system structure to a certain extent. Hence, the volume and weight of the device will increase accordingly. This is not in line with our original intention of lightweight and compact characteristics in our design concept.

The system presented in this paper can address this problem by customizing the 1st auxiliary freeform lens according to the users’ diopters. For users with normal diopters, the optical surfaces, S1 and S10, can be, for example, flat surfaces to ensure that the visual image and see-through image enter the eyes in focus. For users with myopia or hyperopia, we reach diopter adjustment by changing the curvature of surface S1. The curvature of surface S1 is set to negative for myopia and positive for hyperopia so that the entire optical system can meet diopter requirements for different users. Although it seems that the layout shown in Fig. 4(a) is more compact, the 1st auxiliary freeform lens E1 presented in this paper not only benefits to the diopter adjustment, but also the image quality of the virtual light path. Details are discussed in Section 5. Also, because there is a small air gap between the E1 and E2, a reasonable mechanical structural design can realize the disassembly and replacement of E1.

When the user’s diopter changes, the diopter adjustment function can be achieved by replacing auxiliary lens E1. Figure 4(b) shows an example of the freeform prism system that adjusts the diopter by changing the shape of the surface, S1. The positive curvature of surface S1 corrects the user’s hyperopia. Figure 4(c) shows that negative curvature of the surface S1 corrects the user’s myopia. For instance, surface S1 is flat for users with normal vision, and for users with myopia of −4 diopter, S1 is concave and has a radius of curvature of 131.7 mm. For users of different diopters, this design can reduce the cost and space occupancy rate of the freeform prism group and extends the service life. For a more clear explanation, the following optimization process sets the S1 to a flat surface.

Based on the system specifications and design methods outlined in Sections 3 and 4, the optimization process of the OST-HMD optical system is introduced in detail in this section. The optimization of the virtual image light path, correction of distortion, and balance of the system performance attained by the automatic method in the entire FOV are emphasized.

The optimization process has been thoroughly analyzed in a previous paper [14], but a brief introduction is provided here. Based on the previously designed system, an auxiliary freeform lens was added to the light path. By preliminary scaling, the parameters of the initial structure gradually approximated the requirements.

Modeling this system in CODE V, the optimization process is always based on the TIR constraints, structural constraints, and the basic optical definitions such as effective focal length, outlined in Section 4. Unlike the rotationally symmetric system, the freeform prism has only single-sided symmetry. Therefore, the setup method of linear field sampling along the radial direction is no longer applicable, and the freeform prism design must be optimized for half of all FOVs sampled in a rectangular grid. An incremental optimization strategy was adopted. With the improvement in system performance during the optimization process, we gradually increased the number of field samples and the degree of freedom of the surface. The surface type of the prism is converted from spheric to aspheric, then anamorphic, and finally XY polynomial. Compared with the design in the previous paper [26], the present main prism has only two freeform surfaces, S4 and S5, which reduces the difficulty of optimization.

In the imaging optical system, improving the imaging quality is the main task, and the ultimate goal is to obtain an image that is completely similar to the object on the focal plane. However, the actual optical system can only form a perfect image when the object point is paraxial, and a thin beam is observed. The outward expansion of the FOV and aperture destroys the concentricity of the imaging beam and produces various imaging defects; thus, the shape of the image and object cannot be completely similar.

The correction of optical distortion, in a fundamental sense, is to change the relative positional relationship between the image points on the image plane or to rearrange the image points so that the observer or camera can capture an undistorted image. The correction of distortion requires changing the conjugate relationship between the object and image points. A new conjugate relationship between the object and image can be achieved by controlling the positioning of rays reached in the image plane, resulting in a smaller distortion ratio.

Generally, for an optical system with rotational symmetry, only radial distortion should be considered. Figure 5(a) shows a schematic diagram of radial distortion, where hreal is the real image point in the image plane of the specified field, and hideal is the ideal image point of the same field. By controlling the distance between hideal and hreal, the distortion ratio can also be controlled. However, in our design, the off-axis property of the optical system causes irregular distortion. In addition to the radial direction, tangential distortion should be considered. As shown in Fig. 5(b), assuming that an ideal image without distortion is a black grid, the red dots represent the real image points of the sample fields. For a specified field, the ideal image point in the image plane was marked as Pideal, and the real image point position in the image plane was marked as Preal. To control the distortion of our system, the constraint to make the point Preal close to Pideal must be established.

In theory, a freeform surface has a different curvature at each point. Thus, the freeform surface can control the optical path difference, luminous flux, and even the direction and position of the rays according to the image quality requirements more easily. Therefore, the freeform surface can be used to grasp the direction of rays emitted from each FOV and control the position of each image point reached on the image plane.

For an OST-HMD optical system, both the distortion of the virtual image light path and see-through path must be corrected. On the one hand, the freeform system produced large distortion when projecting the image displayed in microdisplay into the human eye. Due to the off-axis property of freeform prisms, the produced distortion is also asymmetry. On the other hand, when users see the external scene through the OST-HMD, the deformation of the real-world scene caused by the see-through distortion critically affects the virtual and real registration of the system.

For the design in our previous paper [26], due to the trapezoidal shape distortion caused by the off-axis property of freeform prisms and the presence of a small amount of lens barrel distortion, the distortion grid in the virtual image light path is as high as 12% in the upper left/right corner, as shown in Fig. 6(a), which is difficult to correct. The distortion of the see-through light path was 1.4%, although a complicated design process was executed, as shown in Fig. 6(b). In addition, to control the asymmetry distortion, the effective focal lengths in the X and Y directions of the optical system are different. Consequently, there is an anamorphic ratio in both the virtual image light path and the light path, which makes the image look slightly wider than the origin, especially for the see-through light path.

However, for the current solution, the optimized distortion of the virtual image light path is now less than 0.6% before electronic correction, while the difference in the distortion rates between the X and Y directions is avoided. Regarding the see-through light path, due to the application of auxiliary lens E1, the distortion of the real scene is greatly decreased to 0.4% after simple optimization is implemented. Moreover, the cancelation of electronic corrections saves computing resources and reduces power consumption. The distortion diagram of the virtual image light path and the see-through light path is shown in Figs. 6(c) and 6(d), respectively, for the presented design.

Further, the MTF of the see-through light path is improved, as shown in Fig. 7. Figure 7(a) shows the MTF plot of the previous design [26], where the value is greater than 0.1 at 50 lp/mm for all sampled fields. The MTF value of the present design is 0.9 at 50 lp/mm for all fields, which implies a better see-through performance.

To further improve the optical performance of the system, the system performance of the entire FOV must be balanced, by continuously adjusting the weight of the sampling field and azimuth. In most cases, the default weights provided by the software will be used for optimization, or a more appropriate set of weights will be assigned based on experience. After each optimization trial, the designer needs to adjust the weight of the sampling field and the azimuth according to the optimization results and design requirements and then use the original constraints and new constraints to optimize the system again to seek the best optimization results. This can be a long and tedious process for optical designers.

Our previous work [49] introduced an automatic image-performance balancing method. An outer loop was added for automatic weight adjustment for optimization. First, we set the initial weights for all the sampled fields and azimuths to an equal value and evaluated the image performance before each optimization trial to calculate the weights for the next trial. The sampled fields and azimuths with performance values lower than the average were assigned higher weights and vice versa. When the exit condition is reached, the loop ends.

When designing a freeform optical system, global optimization is also a way to balance image performance. However, in this study, the design included two freeform optical surfaces; over 100 parameters were defined as variables, and 25 fields were sampled. It requires several minutes to complete a single local optimization loop and requires more than 100 h to finish a global optimization loop. However, by employing the automatic balancing method, the balancing process is completed within half an hour. Finally, through several automatic optimization trials to achieve the performance balance of the entire FOV, the overall optical performance of the system can be improved. Figure 8(a) shows the error function variations for different optimization trials of automatic balancing. The value dropped from 71 for the original design to 50 after 10 trials of optimization, and the rapid descent occurred in the first four to seven trials. After completing all optimization steps, the final system is obtained, and the layout is shown in Fig. 8(b).

The MTF plot of the optical system before and after balancing is shown in Fig. 9. Uniformity of the MTF value for full fields has been greatly improved. Besides, because of the use of a pair of positive and negative lenses, the lateral color aberration is fully corrected.

For a visual system, the relative position between human eye and exit pupil of the OST-HMD is always unstable. Eye shift or rotation caused by the difference in face shape between individuals and other factors should be considered. To evaluate the image performance when the eye shifts in the area of the exit pupil, additional MTF plots are given in Fig. 10. A major assumption is that the pupil size of the human eye is 3 mm under normal light conditions. In the area of the exit pupil, three positions including center, 2.5 mm offset to the right from center, 2.5 mm offset upwards from center, are chosen for evaluation. The results show that the MTF values of all fields are higher than 0.4 at 50 lp/mm, indicating the MTF performance at different positions meets the design requirement.

Tolerance analysis is an essential part of optical design because it is closely related to optical fabrication, alignment, and cost. By carefully evaluating the parameter-variant/image-effect interaction and paying particular attention to the negative and positive aspects of these interactions, we can avoid overdesign and assign tight tolerances only where needed. Such analysis helps determine the acceptable limits for different fabrication and alignment errors.

Unlike the rotationally symmetric system, the tolerance analysis of the freeform system is more complex, and each surface has many optical parameters that would affect the result. In Ref. [27], we introduced the process of tolerance analysis of a system with freeform in detail. For the design presented in this paper, an overall tolerance analysis was conducted using the tolerance values listed in Table 4. The position and tilt of the microdisplay are defined as compensators.Table 4.

Tolerance Items

Figure 11 plots the overall analysis results of the probable changes in MTF values with different cumulative probabilities. The largest probable change in MTF with 99.9% cumulative probability is −0.23. The MTF at 50 lp/mm is higher than 0.17. Meanwhile, the MTF with 84.1% cumulative probability is higher than 0.29.

Among the different tolerance errors, delta sag at a clear aperture (DLS) is more sensitive than the others, while the thickness of the surfaces is insensitive. The performances of F4, F6, and F23 have the greatest impact.

The system was fabricated using a molding approach. From Fig. 12(a), an exploded view of the optics module with all components is provided. The overall appearance is shown in Fig. 12(b). The main prism E2 and auxiliary lens E1 were connected by a mechanical structure while maintaining air separation. The main prism and correcting plate were glued with UV glue, and the lens holder fixed the microdisplay, lens-01 (E3), and lens-02 (E4). The total weight of the display module is 12.8 g, which meets the weight requirement of the OST-HMD.

To demonstrate the virtual and see-through light path image quality of the OST-HMD, simple tests are implemented. A commercial camera is used to simulate the human eyes and capture the displayed image transmitted through the OST-HMD system. The camera was placed in front of the optical module; the stop aperture and optical axis of the camera coincide with the exit pupil and viewing axis of the optical module.

A image resolution test chart shown in Fig. 13(a) was displayed at the microdisplay. Figure 13(b), a clear and nondistorted picture, was obtained, expressing the good virtual image performance of the optical module. Figure 13(c) shows the result of the fusion of a virtual cup and a real cup, demonstrating this module’s potential applications in augmented reality.

In this study, we designed an OST-HMD system using a combination of three wedge-shaped freeform prisms and two lenses. The system achieves a diagonal FOV of 45.3° and an F/# of 1.8, with an EPD of 12mm×8mm, and an ERF of 18 mm. The overall size of the optical system is 30mm(width)×40mm(height)×14mm (thickness), and the system has a weight of 12.8 g per eye, which meets the requirements of compact structure and light weight. Although the thickness of the optical element is up to 14 mm, the total thickness of the OST-HMD system is much less than that of the other solutions listed in Table 1 with similar FOV and EPD. The light efficiency of the virtual image light path can be up to 50%, which is much higher than that of other optical solutions, reducing the heat generation and making the system conducive to the wearing experience. Almost negligible distortion not only reduces the energy consumption due to electronic correction, but also guarantees virtual and real registration. Changing the radius of the first surface, S1, of the auxiliary lens, E1, allowed the optical system to meet the user’s diopter requirements. The performance of the optical system was analyzed and was accompanied by a demonstration of an experimental prototype. The results indicate that the system is well suited to OST-HMD applications. We will develop a smaller FOV but much thinner OST-HMD system with freeform optics in a future study, and we believe the design will also greatly promote the AR industry as well.

Acknowledgment. We thank Synopsys for providing the educational license of CODE V.