# Anti-Fatigue Glasses Based on Microprisms for Preventing Eyestrain

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## Abstract

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## 1. Introduction

## 2. Determination of the Parameters of Microprismatic Glasses

#### 2.1. Structures of Anti-Fatigue Glasses Based on Microprisms

#### 2.2. Prismatic Diopter of Anti-Fatigue Glasses

#### 2.3. Physical Phenomena with the Anti-Fatigue Microprismatic Glasses

_{0}stands for the length of the bottom of the prism unit (i.e., the pitch width), L

_{0}stands for the height of the prism unit, α and β are the angles defining the prism shape, and n

_{1}and n

_{2}are the refractive indexes of the microprism and the surroundings, respectively. The parameter that decides the prismatic diopter of the prism is α, and β is related to the technological requirement of reducing stray light. According to our previous experience [22], β should be set as 2°–3° for reducing stray light.

_{0}is the width of the diffractive slit when a single prism unit is considered, I

_{0}is the initial optical intensity, and ${\left(\frac{\mathrm{sin}a}{a}\right)}^{2}$ is typically referred to as the single-slit diffraction factor.

_{1}is the width of the interference slit between two diffractive beams from prism units, and ${\left(\frac{\mathrm{sin}Nb}{\mathrm{sin}b}\right)}^{2}$ is typically referred to as the interference factor between multiple slits.

_{0}~ 100–200 μm the expansion of optical images after the microprism became very large (Δγ ~ 0.2°–0.4°) compared with the prism deflection angle γ ≈ 5.2° for a pupil distance of 64 mm and an observation distance of 350 mm. The smallest resolution angle of a normal eye is usually 0.017°, therefore W

_{0}should be around 600 μm. The value N is defined by the size of the microrelief area, which is illuminated by a laser beam. In our calculations, if the typical value of the pitch width is W

_{0}= 600 µm, then N = 4 is a reasonable value that corresponds to the diameter of the laser beam. The working wavelength λ is chosen as 6328 nm.

_{0}= 530 μm, the corresponding angle is just 0.017°; therefore, the pitch width W

_{0}should be larger than 530 μm. However, if W

_{0}is too large the anti-fatigue microprismatic glasses will be inconvenient for wearing due to visible streaking of the images.

_{0}= 600–800 μm. For lower pitches the microprisms would distort the observed optical images. For larger pitches the anti-fatigue glasses would not be attractive from a cosmetic viewpoint because the structures of the microrelief become clearly visible.

## 3. Fabrication of Anti-Fatigue Microprismatic Glasses

_{0}) and the height of the prism unit (L

_{0}). On the basis of the measured results we can also characterize the surface finish (R

_{a}) of the fabricated microprism by numerical analysis. The surface finish (R

_{a}) can be calculated by the contour arithmetic mean deviation:

## 4. Measuring System of the Prismatic Diopter

_{E}) of 10 mm on the screen with a distance (L

_{E}) of 1000 mm from the prism to the screen corresponds to a prismatic diopter of 1.0 prismatic diopter (Δ); therefore, for any deflection angle γ the prismatic diopter can be easily calculated as Δ = 100 (l

_{E}/L

_{E}) [21].

_{max}) corresponding to the largest prismatic diopter as the reference value; therefore, the rotation angle should be increased depending on the increase in prism strength for prisms with smaller Δ.

_{30}= 16.69924° according to the definition of prismatic diopter. In our measuring system, the prism with 30.0 Δ is taken as the standard prism with the largest value of γ

_{max}; therefore, for the microprism with 30.0 Δ the rotation angle of the rotating element is set to zero (0°). For all other microprisms, the values of the rotation angle (θ) should be obtained for which the deflection angle γ = γ

_{30}= 16.69924°, depending on the prismatic diopter for all tested microprisms. The dependence of the prismatic diopter on the rotation angle θ was investigated [21,22] and shown in Figure 9.

_{E}to 250 mm and in turn reduce the size of the measuring system. The adjustable diaphragm in front of the first reflector must be set in the direction of γ

_{30}, because we took the largest prismatic diopter as the reference value. In addition, the laser must exit horizontally and incident on the flat surface without microrelief to avoid measurement error; moreover, the element holder can only be rotated in one direction to improve the measuring accuracy. Figure 10b displays the photo of the developed compact measuring system for prismatic diopters of prisms or microprisms.

_{30}= 16.69924° by rotation of the prism, because the reflection angle of the laser beam inside the prisms exceeds the critical reflection angle in this case [24], which for PMMA with refractive index of 1.492 is calculated to 39.74° [21]. It means the beam is totally reflected inside the prism and cannot be deflected to the stated angle of γ

_{30}= 16.69924°. For example, for a prism with a prismatic diopter of 1.0 Δ the largest possible rotation angle is θ = 77.76°, which corresponds to a deflection angle (γ) of 10.66°. For a prism with a prismatic diopter of 2.0 Δ the largest possible rotation angle θ = 72.598°, which corresponds to a deflection angle (γ) of 14.94°.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Objective prismatic diopter for anti-fatigue glasses from the consideration of geometrical optics.

**Figure 4.**Diffraction, interference, and total effect for the microprism with W

_{0}= 600 μm, and with 2.0 Δ for (

**a**) and 7.0 Δ for (

**b**).

**Figure 5.**Diffraction, interference, and total effect for the microprism with 4.0 Δ and with W

_{0}= 530 μm for (

**a**) and W

_{0}= 800 μm for (

**b**).

**Figure 7.**(

**a**) Photograph of a sample of the PMMA microprism we fabricated; (

**b**) partially enlarged view of the microrelief under an optical microscope; (

**c**) photograph of the fabricated PMMA anti-fatigue glasses based on microprisms for preventing eyestrain.

**Figure 8.**Measured results for the structure of a fabricated PMMA microprism by SEM (

**a**) and by stylus profiler (

**b**).

**Figure 9.**Dependence of prismatic diopter on the difference in rotating angle for prisms with different prismatic diopter (PD).

**Figure 10.**(

**a**) Scheme of the developed compact measuring system for testing the prismatic diopter of prisms; (

**b**) photograph of the developed compact measuring system.

Pitch Width (W_{0}, μm) | Angle Related to Diffraction Only (°) | Angle Related to Interference Only (°) | Angle with Total Effect (°) |
---|---|---|---|

300 | 0.118 | 0.03 | 0.032 |

400 | 0.088 | 0.022 | 0.022 |

500 | 0.071 | 0.018 | 0.019 |

530 | 0.066 | 0.017 | 0.017 |

600 | 0.061 | 0.015 | 0.015 |

700 | 0.05 | 0.013 | 0.013 |

800 | 0.045 | 0.011 | 0.012 |

1000 | 0.035 | 0.0087 | 0.0098 |

Tested Samples | Pitch Width (W_{0}, μm) | Height of Prism Unit (L_{0}, μm) | Surface Finish (R_{a}, nm) |
---|---|---|---|

pressing stamper | 600.55 | 54.53 | 147.41 |

microprism 1# | 600.72 | 54.29 | 132.77 |

microprism 2# | 600.62 | 55.84 | 165.15 |

microprism 3# | 600.12 | 55.21 | 134.61 |

microprism 4# | 600.09 | 55.32 | 126.28 |

microprism 5# | 600.23 | 55.50 | 173.86 |

Tested Samples | Rotating Angle (θ, °) | Prismatic Diopter (Δ) |
---|---|---|

microprism 1# | 61.34 | 5.0 |

microprism 2# | 61.45 | 5.0 |

microprism 3# | 61.28 | 5.0 |

microprism 4# | 61.17 | 5.0 |

microprism 5# | 61.35 | 5.0 |

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**MDPI and ACS Style**

Le, Z.; Antonov, E.; Mao, Q.; Petrov, V.; Wang, Y.; Wang, W.; Shevkolenko, M.; Dong, W.
Anti-Fatigue Glasses Based on Microprisms for Preventing Eyestrain. *Sensors* **2022**, *22*, 1933.
https://doi.org/10.3390/s22051933

**AMA Style**

Le Z, Antonov E, Mao Q, Petrov V, Wang Y, Wang W, Shevkolenko M, Dong W.
Anti-Fatigue Glasses Based on Microprisms for Preventing Eyestrain. *Sensors*. 2022; 22(5):1933.
https://doi.org/10.3390/s22051933

**Chicago/Turabian Style**

Le, Zichun, Evhen Antonov, Qiang Mao, Viacheslav Petrov, Yuhui Wang, Wei Wang, Marina Shevkolenko, and Wen Dong.
2022. "Anti-Fatigue Glasses Based on Microprisms for Preventing Eyestrain" *Sensors* 22, no. 5: 1933.
https://doi.org/10.3390/s22051933