本研究提出一套創新的多自由度再繞射式光柵干涉儀，用以同時量測五維度位移及旋轉角度變化量。此套系統是以光柵為技術核心進行開發，同時整合外差干涉術、光柵干涉術、再繞射光路及共面偵測技術等設計之優勢，使系統具備高解析度、高穩定度及五自由度的量測能力。
此套再繞射式光柵干涉儀是透過「再繞射」的光路設計，使雷射光束產生兩次的繞射效應，進而引入加倍的相位變化量，有效的提升光柵干涉儀的系統解析度，此外，一般光柵干涉儀需要於各軸向增加偵測架構，亦或是選用二維光柵等方式達成多維度的量測；而此套創新的再繞射式光柵干涉儀透過光路設計及共面偵測技術的配合，在不改變光學架構下，加入側向位移分光器及光感測器兩種光學元件，方能於光柵上形成三個偵測點，使系統在少量光學元件下具備五自由度(x, z, θx, θy, θz)的精密量測能力，具備不離焦偵測及高光使用率等優勢，成功突破目前多自由度光柵干涉儀所面臨的瓶頸。
為了驗證本研究所提出之多自由度再繞射式光柵干涉儀的可行性及其系統性能，我們進行了一系列的驗證實驗，並將本研究所開發的光柵干涉儀實驗結果與平台內建的電容式位移計及線性光學尺所量測到的結果相比較。由實驗結果證明，此套再繞射式光柵干涉儀僅需一個待測光柵，即可同時提供五自由度位移及旋轉角的量測訊息，其實際位移與旋轉角度的解析度分別約為3 nm與100 nrad，重複性分別優於0.62 nm及63 nrad，量測速度極限可達160 μm/s，具備優異的量測性能，可廣泛應用於精密量測、工具機業及自動化光學檢測等場合中。

In this study, a recurring-diffraction grating interferometer for multi-degree-of-freedom measurement is proposed. The recurring-diffraction type grating interferometer is developed by combining the advantages of heterodyne interferometry, grating interferometry, recurring diffraction optical configuration, as well as the coplanar detection technique. It has the capability of measuring in five degrees-of-freedom (DOF) with high resolution and stability.
The proposed system takes advantage of a “recurring-diffraction” optical configuration, which directs diffracted light to pass through a grating twice without additional optical components, thereby doubling the phase change induced by grating displacement, effectively improving the resolution of the grating interferometer. In addition, the generally grating interferometer needs to increase the detection structures in each axial, or select a two-dimensional grating to achieve multi-dimensional measurement. Furthermore, the
This innovative recurring-diffraction interferometer through the incorporation of two optical
component. Three detection points are formed on the system, so that the system has the precision measurement capability of five degrees of freedom (x, z, θx, θy, θz) with few optical components, and has the advantages of no defocus detection and high light utilization rate, and successfully overcome the problem of grating interferomter multi degree of freedom in nowadays.
In order to verify the feasibility and performance of the proposed recurring-diffraction grating interferometer, a series of experiments were conducted, with the measurement results obtained from the proposed system compared with the built-in capacitive sensor and linear encoder of commercial positioning stages. As displayed in the results, the proposed recurring-diffraction grating interferometer has the ability to perform precision displacement and rotation measurement in five DOFs simultaneously without needing to change the optical configuration with resolutions for displacement and rotation measurement of 3 nm and 100 nrad, and the repeatability better than 0.62 nm and 63 nrad, respectively. The maximum velocity for displacement measurement can reach 160 μm/s. The proposed grating interferometer has excellent measurement properties, and is well-suited for applications within precision manufacturing, tool machine industry, automatic optical measurement, nanotechnology, semi-conductor technology and other related fields.

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