彈性立方相位板延伸景深之研究

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李祈鋒(Chi-Feng Lee) 查詢紙本館藏

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光電科學與工程學系

論文名稱

彈性立方相位板延伸景深之研究
(A Study of Flexible Cubic Phase Plate for Extension of the Depth of Field)

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摘要(中)

傳統的光學系統的景深可以藉由降低光焦度、增加最小模糊圈容許度或是提高系統複雜度等方式來延伸。隨著繞射理論的興起，近年來許多研究開始發展波前編碼技術，許多研究利用了各種形式的相位元件，放置於孔徑光闌或出瞳，以延伸非同調光學系統中的景深。然而，波前編碼技術仍遭遇了一些困難，例如，將相位元件放置在孔徑光闌或出瞳的位置並非適用於各種系統，因為這會導致相位元件與系統機構或相鄰的透鏡互相碰撞。另外，若出瞳的位置並非位於後焦區域，則無法正確的調製波前。因此，在本論文中，本研究以立方相位板為例，通過調整立方相位板的立方係數與折射率，來使該元件可以彈性化地改變放置位置，或是於透鏡表面調變波前，同時保有相同的編碼強度，以維持正確的編碼結果。本論文以反射式、穿透式與投影式的光學系統來呈現彈性立方相位板與波前編碼之應用。首先，以反射式望遠鏡為例，立方相位板的位置改變後，該元件的直徑縮小了近三倍，並且多項式表面的立方係數提高了兩個數量級，因此，在尺寸縮小與精度降低的情況下，以減輕製造困難。再來，對顯微鏡物鏡的例子來說，本研究於透鏡表面上使用立方相位調製用以替換單個孔徑光闌的立方相位板，解決了在某些情況下會與光學元件和機械裝置發生碰撞之情形，並且降低了組裝難度。所以，具有靈活性且不損失照明水平的顯微鏡亦可以提高顯微學應用的效率。然而，考慮到離軸像差之劇烈影響，立方相位板應用在非近軸視場角的光學系統時，其效能相當受限。因此，本論文以雙高斯系統為例，提出了分離立方相位板於不同透鏡表面之方法。此方法利用不同的分配因子來調整不同的透鏡表面的編碼強度，以使得相位變化得以接近獨立於各個視場。所以，在立方相位板的位置、折射率於立方係數皆可調整的情況下，本論文以理論與應用呈現了彈性立方相位板延伸景深的可行性。最後，在不受限於立方相位板必須放置在孔徑光闌的限制條件下，本論文將立方係數應用至凹面鏡上以呈現波前編碼穿透式顯示器之應用，同時延伸投影影像之景深，該研究利用反向波前編碼程序使得人眼無需來回對焦於物體與投影影像以提高安全性。

摘要(英)

The depth of field (DOF) in traditional optical systems is difficult to be extended without considering the reduction of the optical power or increase of the system complexity. In recent years, with the rise of diffraction theory, many researchers developed wavefront coding (WFC) technique and employed various forms of phase elements to extend the DOF by placing it in the aperture stop or exit pupil of an incoherent optical system. However, the WFC technique encounters some issues. For example, the phase element placed in the aperture stop is not physically possible for various systems since it will cause the phase element to collide with the mechanical structure or adjacent lenses. In addition, if the exit pupil with the phase element is not located in the region of the back focal length, the wavefront cannot be modulated correctly. Therefore, this thesis takes the cubic phase plate (CPP) as an example by adjusting its position, cubic coefficient, and refractive index to accomplish the application of flexibility; The CPP can be flexibly changed in its placement position while maintaining the same coding strength to get the correct coding result. First, taking a reflecting telescope as an example. Once the position of the CPP is changed, the diameter of the CPP is reduced by nearly three times, and the cubic coefficient of the polynomial surface is increased by two orders of magnitude. Therefore, the difficulty of manufacturing is eased when the precision is reduced. Second, for the example of the microscope, this thesis employs the CPP on the surface of the optical components and eliminates the CPP in the aperture stop, which solves the problem of collisions with optical components and mechanical structure in some cases, thus the assembly difficulty can be reduced. Therefore, the microscope with flexibility can also improve the efficiency of microscopy applications without loss of illumination level. However, when the CPP is employed in these optical systems, its performance is quite limited due to the severe effects of the off-axis field of view and aberrations. Therefore, this thesis proposes a method to separate the CPP and assign it on different surfaces of lenses by taking the Double-Gauss system as an example. Different distribution factors are applied to adjust the coding strength of different surfaces of lenses with cubic coefficients so that the phase function is nearly independent of the field of view. Therefore, under the condition that the position of the CPP, refractive index and cubic coefficient can be adjusted, this thesis presents the feasibility of the flexibility of the CPP to extend the DOF. Finally, without the restriction that the CPP must be placed in the aperture stop, this thesis also presents the application of a WFC see-through display to extend the DOF of the projected image by applying the cubic coefficient in the concave mirror. This research uses the inverted WFC process, the technique eliminates the requirement that the human eyes focus between the object and projected image, meanwhile, the safety can be improved.

關鍵字(中)

★ 波前編碼
★ 光學設計
★ 延伸景深
★ 立方相位板

關鍵字(英)

★ Wavefront coding
★ Optical design
★ Extended depth of field
★ Cubic phase plate

論文目次

中文提要 …………………………………………………………… i
英文提要 …………………………………………………………… iii
誌謝 …………………………………………………………… v
目錄 …………………………………………………………… vi
圖目錄 …………………………………………………………… viii
表目錄 …………………………………………………………… x
符號說明 …………………………………………………………… xi
一、緒論……………………………………………………… 1
1-1 研究背景………………………………………………… 1
1-2 研究目的………………………………………………… 9
二、研究理論………………………………………………… 12
2-1 景深理論………………………………………………… 12
2-2 波前編碼理論…………………………………………… 17
2-3 彈性立方相位板之應用………………………………… 27
2-3-1 立方相位板之位置……………………………………… 27
2-3-2 立方相位板之分離……………………………………… 31
2-3-3 點擴散函數的相似性評估……………………………… 35
三、成像系統之光學設計與模擬…………………………… 36
3-1 反射望遠鏡之範例……………………………………… 37
3-1-1 反射望遠鏡之鏡頭架構………………………………… 37
3-1-2 立方相位板的位置和立方係數………………………… 39
3-1-3 影像處理………………………………………………… 46
3-2 顯微鏡之範例…………………………………………… 50
3-2-1 顯微鏡之架構…………………………………………… 50
3-2-2 立方相位板的位置和立方係數………………………… 51
3-2-3 影像處理………………………………………………… 56
3-3 雙高斯鏡頭之範例……………………………………… 60
3-3-1 立方相位板之拆解……………………………………… 62
3-3-2 影像處理………………………………………………… 67
四、波前編碼穿透式顯示器………………………………… 70
4-1 穿透式顯示器之景深…………………………………… 70
4-2 波前編碼穿透式顯示器之設計………………………… 71
4-3 波前編碼穿透式顯示器之模擬結果…………………… 75
五、結論……………………………………………………… 80
參考文獻 …………………………………………………………… 83

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指導教授

李正中(Cheng-Chung Lee)

審核日期

2021-8-31

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