Index Error Estimation Using Fourier Analysis on Grating Disks

The patent uses a single detector to capture signals from multiple virtual grating disks created by moiré patterns. Instead of physically arranging multiple detectors at different angular positions, the system creates optical copies of the grating disk pattern through moiré interference, allowing one detector to obtain information that would otherwise require multiple detectors. This resolves the contradiction by maintaining measurement precision while reducing device complexity.

The patent introduces a moiré pattern as an intermediary between the grating disk and the detector. The moiré pattern acts as a mediator that transforms the spatial distribution of index marks into a form that can be captured by a single detector. By using the moiré pattern as an intermediary, the system achieves the function of multiple detectors with only one physical detector, thereby improving measurement precision without increasing device complexity.

The patent creates multiple virtual grating disk patterns through moiré interference, allowing a single detector to capture signals that would otherwise require multiple detectors positioned at different angular locations. This copying approach enables the system to identify higher degree Fourier components without requiring extremely precise rotation mechanisms or multiple detectors, thus reducing manufacturing precision requirements while maintaining device simplicity.

The patent replaces the mechanical approach of using multiple detectors physically arranged at different angular positions with an optical approach using moiré patterns. Instead of mechanically positioning multiple detectors with high precision, the system uses optical interference patterns to achieve the same measurement function, thereby reducing manufacturing precision requirements for the rotation mechanism while keeping device complexity low.

The patent uses moiré patterns to create multiple virtual grating disk images that appear to be arranged at even angular distances, but are actually generated from a single physical grating disk. This copying mechanism allows the system to achieve index error calibration accuracy equivalent to having multiple detectors at different positions without requiring additional grating disk material, thus improving measurement precision while minimizing loss of substance.

The patent merges the functions of multiple detectors into a single detector by using moiré patterns to combine the optical signals that would otherwise require separate detectors. By merging the detection functions, the system achieves the same calibration accuracy without needing multiple detectors or additional grating disk areas, thereby improving measurement precision while reducing loss of substance.