一種新的剪切波前分析儀開發

Development of a new lateral shearing wavefront analyzer

林昕叡(Sin-Ruei Lin)

指導教授 ： 李世光

國立臺灣大學/工學院/應用力學研究所/碩士(2024年)

https://doi.org/10.6342/NTU202403670

摘要

波前感測裝置在光學測量領域扮演著相當重要的角色，其優點為非接觸式與高解析度。本團隊過去曾經開發一款利用剪切干涉片進行橫向剪切干涉的光波前測量裝置SPARROW (Shear Phase Analyzer, Reflective/Reflective Optical Wavefront)，其內部有一直角旋轉機構以確保光線入射出射保持平行，並且使用一自感應熱阻絲之熱膨脹轉動直角旋轉機構以產生相位移法所需要之干涉相位改變。SPARROW之優點為其較大的測量波前動態範圍與便於攜帶的機構大小。然而，由於剪切干涉需要測量兩相互垂直方向之干涉條紋，SPARROW之測量需要透過旋轉整個感測器的方式分別對兩方向干涉條紋進行量測，對於測量的精準性與時間長度造成影響。
本研究採用前述直角旋轉機構產生剪影干涉，該機構由垂直的兩個面組成，其中一面為一片鏡子，另一面為一剪切干涉片，兩面相連處為一旋轉軸。該架構類似一回射器，確保入射的光線與出射的光線在任意入射角度下，出射光永遠保持平行。本研究並提出創新想法：使用光波前方向與極化方向同時綁定的方式，進行同時測量兩方向之干涉條紋影像。首先將入射光波前分為兩道，並且使用一組K-mirrors將其中一道之光波前與極化方向同時旋轉90度，接著使用一PBS將極化方向與波前方向進行綁定，最後在經由直角旋轉機構進行干涉後由另一PBS將兩方向之干涉分開分別使用兩相機記錄。如此一來，兩方向之干涉條紋可以同時測得，增快測量的過程；並且由於移除了整體旋轉的過程，也確保了測量的穩定性。
本研究亦針對過往使用的重建算法做出調整，裝置中的剪切干涉片產生干涉條紋，採用四步相移法配合裝置的熱電阻絲調控相移的相位角，取得條紋圖後計算獲得包裹相位，包裹相位的邊界需利用自然填充法將遺失的資訊填充補回，方能進行傅立葉擬合波前重建獲得誤差最小之波前。最後設計不同的實驗驗證本裝置，重複性最差可達PV(峰對峰)值相差1/4.79λ、方均根值相差1/ 112λ；動態範圍與理論值94.173至10.936 波長相差不到一個波長；準確度在量測了除去Coma之各種由可變形鏡產生之低階像差誤差，其rms誤差均在1/17個波長以內，PV誤差均在1/3個波長以內。最後並完成以本儀器進行血液抹片之初步觀察實驗，證明本系統具有良好的量測性能與未來應用於生醫量測領域之可能性。

關鍵字

橫向剪切干涉 ； 光波前測量 ； 光波前重建

並列摘要

Wavefront sensing devices play a crucial role in the field of optical measurement, offering advantages such as non-contact measurement and high resolution. Our team previously developed a wavefront measurement device, SPARROW (Shear Phase Analyzer, Reflective/Reflective Optical Wavefront), which utilizes a shear interferometer for lateral shearing interferometry. SPARROW features an internal right-angle rotation mechanism to ensure that the incident and outgoing light beams remain parallel. It also uses a thermally induced self-sensing thermal resistance wire to produce the phase changes required for phase-shifting interferometry. The advantages of SPARROW include a large dynamic range for wavefront measurement and a compact, portable size. However, since shearing interferometry requires measuring interference fringes in two orthogonal directions, SPARROW must rotate the entire sensor to measure fringes in each direction separately, affecting measurement accuracy and time.
This study employs the aforementioned right-angle rotation mechanism to generate shear interferometry. The mechanism consists of two perpendicular surfaces, one being a mirror and the other a shear interferometer, with a rotation axis at their intersection. This setup is similar to a retroreflector, ensuring that the incident and outgoing light beams remain parallel regardless of the incident angle. We propose an innovative approach: binding the wavefront direction with the polarization direction to simultaneously measure interference fringe images in both directions. The incident wavefront is first split into two beams, and a set of K-mirrors is used to rotate the wavefront and polarization direction of one beam by 90 degrees. Then, a PBS is used to bind the polarization direction with the wavefront direction. After interference via the right-angle rotation mechanism, another PBS separates the two directions of interference, which are then recorded by two cameras. This allows for simultaneous measurement of interference fringes in both directions, speeding up the measurement process and ensuring stability by eliminating the need for overall rotation.
We also modified the reconstruction algorithm previously used. The shear interferometer in the device produces interference fringes, and the four-step phase-shifting method is employed with the thermal resistance wire to control the phase shift angle. After obtaining the fringe pattern, the wrapped phase is calculated. The boundaries of the wrapped phase need to be filled using natural extension methods to recover the missing information before performing Fourier wavefront reconstruction to obtain the wavefront. Various experiments were designed to validate the device. The repeatability achieved a peak-to-valley (PV) of 1/4.79λ and a root mean square (RMS) of 1/112λ. The dynamic range deviation from the theoretical value was less than one wavelength, ranging from 94.173 to 10.936 wavelengths. The accuracy, when measuring various low-order aberrations produced by a deformable mirror with the removal of coma, showed RMS errors within 1/17 wavelength and PV errors within 1/3 wavelength. Finally, preliminary observation experiments of blood smears using the device demonstrated its excellent measurement performance and potential for future applications in biomedical measurement.

並列關鍵字

lateral shearing wavefront sensing ； wavefront sensing ； wavefront reconstruction

參考文獻

S. Kang et al., "High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering," Nature Communications, vol. 8, no. 1, p. 2157, 2017/12/18 2017, doi: 10.1038/s41467-017-02117-8.

J. B. Shohani, M. Hajimahmoodzadeh, and H. Fallah, "Using a deep learning algorithm in image-based wavefront sensing: determining the optimum number of Zernike terms," Opt. Continuum, vol. 2, no. 3, pp. 632-645, 2023/03/15 2023, doi: 10.1364/OPTCON.485330.

K. M. Hampson, J. Antonello, R. Lane, and M. Booth, "Sensorless Adaptive Optics," 2020 2020, doi: 10.5281/ZENODO.4065529.

A. S. De Vany, "Using a Murty Interferometer for Testing the Homogeneity of Test Samples of Optical Materials," Appl. Opt., vol. 10, no. 6, pp. 1459-1460, 1971/06/01 1971, doi: 10.1364/AO.10.001459.

S. Velghe, J. Primot, N. Guerineau, M. Cohen, and B. Wattellier, "Optical Systems Design 2005," pp. 596512-596512, 09/30 2005.