It should be noted that, regarding the concept of the in-situ pitch measurement, all the experiments described in this paper have been carried out in an ordinary laboratory room condition where the optical setup is not shielded from external disturbances such as illumination with fluorescent lights. Methods for In-Situ Measurement of the Grating Pitch with a Diffracted Optical Frequency Comb Laser  
Methods for measurement of the grating pitch with diffracted laser beams are based on the light diffraction equation that can be expressed as follows [19]:  
\[P\sin\theta_{\text{in}}+P\sin\theta_{\text{diff}}=m\lambda \tag{1}\]where \(P\) is the grating pitch, \(\theta_{\text{in}}\) is the angle of incidence of the measurement laser beam, \(\theta_{\text{diff}}\) is the angle of diffraction of the \(m\)th-order diffracted beam, and \(\lambda\) is the light wavelength of the measurement laser beam. It should be noted that \(\theta_{\text{in}}\) and \(\theta_{\text{diff}}\) are defined with respect to the normal of the grating surface. Figure 1a shows a schematic of the setup for measurement of the pitch deviation of a grating. The setup is mainly composed of a monochromatic laser source, a rotary table equipped with a high-precision rotary encoder, and a detector unit (not indicated in the figure). A scale grating can be mounted on the rotary table for pitch measurement. In the setup, a collimated laser beam from the laser source is projected onto the grating surface to generate diffracted beams. The configuration where \(\theta_{\text{in}}\) becomes equal to \(\theta_{\text{diff}}\), as shown in Figure 1a, is referred to as the Littrow configuration [20]. Under the condition of the \(m\)th-order Littrow configuration with the Littrow angle \(\theta_{m}\), \(\theta_{\text{in}}=\theta_{\text{diff}}=\theta_{m}\), and the following equation can be obtained from Equation (1):  
\[P=\frac{m\lambda}{2\sin\theta_{m}} \tag{2}\]  
According to the above equation, the parameters need to be obtained for the calculation of \(P\), \(\theta_{m}\) and \(\lambda\). Since \(\lambda\) can be treated as a known parameter, the grating pitch \(P\) can be evaluated by measuring \(\theta_{m}\) in experiments. By rotating the grating under inspection with a rotary table equipped with a high-precision rotary encoder, multiple diffracted beams can be observed. For the detection of diffracted beams, image sensors such as a charge-coupled device (CCD) are often employed in the detector unit. In most cases, the number of diffracted beams available for pitch measurement is quite limited when employing a monochromatic laser source. For example, in the case where a scale grating having a nominal pitch of 1000 nm is evaluated with a laser beam having a light wavelength of 633 nm, the maximum \(m\) becomes 3; namely, only six diffracted beams (three positive diffracted beams and three negative diffracted beams) can be obtained. It should also be noted that the area to be irradiated by the measurement laser beam could vary with the increase of \(m\). Namely, the grating pitch \(P\) evaluated by the diffracted beams with different diffraction orders could be from a different area on the scale grating. These issues can be addressed by the method with an optical frequency comb laser [17]. Figure 1b shows a schematic of the optical setup for pitch measurement with an optical frequency comb laser. When the collimated laser beam of an optical frequency comb is projected onto a scale grating, the group of the positive first-order diffracted beams emanating from the projected area can be obtained [21]. It should be noted that the group  
Figure 1: Laser diffraction method for measurement of a grating pitch: (**a**) Conventional method with a single-mode laser; (**b**) Proposed method with a mode-locked laser. of the negative first-order diffracted beams and those of the higher-order diffracted beams are not indicated in the figure for the sake of simplicity.