Defects such as scratches and dust on the surfaces of optical components in interferometers can generate diffraction ring coherent noise in interferograms, which can significantly affect measurement accuracy. To address this issue, this study introduces an extended-light-source method in which the coupling angle of a multimode fiber is altered. By controlling the coupling angle of the multimode fiber after the parallel beam passes through the rotating frosted glass, the proposed method effectively minimizes the effects of scattering and coherent noise. This approach provides a valuable contribution to the theory of extended light sources based on multimode fibers. The derivation and validation of the range of fiber incident angles at the location exhibiting the strongest signal-to-noise ratio (SNR) of the interferometric signal offer important guidance for installing and calibrating interferometers and other optical instruments utilizing this light-source configuration.

In this study, the objectives of eliminating coherent noise and improving the SNR of interference fringes in a composite extended source based on multimode fibers are explained. With a change in the coupling angle in the multimode fiber, the shape and size of the light beam emitted from the fiber end change accordingly. When the coupling fiber angle is adjusted, the free degree of the composite-light-source speckle increases, leading to a decrease in system speckle contrast. However, the size of the extended source affects the contrast of the interference fringes. Based on the formula for obtaining the interferometric SNR, it is known that changes in the scattering contrast and interference fringe contrast affect the SNR of the entire extended light source. In this study, the critical incident angle at which the light beam emitted from the fiber end becomes a hollow beam is derived through calculations.

The Zemax OpticStudio software is used to simulate the fiber-end optical field. In the non-sequential mode, a Gaussian light source is set to enter at different incident angles along the x axis. A detection viewer is used to observe changes in light-field distribution. The change in the output field is calculated at different incident angles based on the formula of the light beam emitted from the fiber end. Simulations and calculations are performed to investigate the effects of different fiber incident angles on the fiber output light-field distribution. The detector parameters are then adjusted, the light-field distribution emitted from the fiber end is recorded, and the number of speckle fields is characterized using the average value of the image gradient magnitude.

To verify further the correctness of the theoretical and simulation results, an experiment is conducted on an interferometer with a diameter of 25.4 mm using a multimode fiber with a core diameter of 1 mm. The light-field distribution at the fiber output port is analyzed at different incident angles using a beam quality analyzer, and a wavelength phase-shifting measurement is performed on the measured mirror.

When light is coupled via a multimode fiber at different incident angles, the changing rules of the optical field distribution at the fiber output are the same in the simulation and experiment, as shown in Figs. 5 and 10, respectively. As the incident angle increases, the output light beam changes from a Gaussian distribution to a hollow disc. The interference SNR is maximized when the speckle contrast exhibits a minimum value, and the position of the minimum point is approximately midway between the calculated critical angle of the hollow beam and the normal incident angle. As Table 3 shows, when the angle of the incident multimode fiber is within the range of -3°?2° following a reduction in the temporal coherence of the beam (accomplished by rotating the ground glass), the SNR of the interferometric signal increases from 4.433 dB at normal incidence (0°) to 6.219 dB, which is an increase of 40.3%. In addition, the scattering contrast decreases from 0.333 (the highest level) to 0.204, and the coupling angle is -2° at the highest SNR. This coupling angle is also between the positive incident angle and the critical angle of emergence of the hollow beam, which is consistent with the calculation. It should be noted that the actual position of the hollow beam may deviate from the calculated value because of the fiber status. However, this does not affect the position of the maximum point of the speckle contrast. This position is used to approximate the position of the hollow beam, which in turn is used to determine the position of the minimum point.

Theoretical derivation and simulation experiments prove that when the angle of parallel beam coupling in a multimode fiber is adjusted to the approximate middle position between the normal incidence and critical value, scatter and coherent noise can be suppressed and the SNR of the interferometric signal can be improved. This study also refines the theory of extended light sources based on multimode fibers. In addition, the derived calculation of the position range at the highest SNR provides a useful reference and guidance for mounting optical instrument systems such as interferometers.