Optical Surface Characterization via Iterative Error Separation
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Solution Overview
Problem
Existing methods for characterizing the surface shape of optical elements, particularly in microlithographic projection exposure apparatuses, face challenges in accurately separating test object errors from test set-up errors, especially when the surface is not rotationally symmetrical over its entire area.
Innovation Solution
A method involving interferometric measurements with test object rotation, where multiple measurement series with different numbers of rotational positions are conducted, and the results are evaluated using an iterative process to separate errors of different orders, allowing for reliable testing of non-rotationally symmetrical surfaces.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a single measurement series with fixed number of rotational positions is used, then the measurement process is simple and fast, but the ability to separate test object errors from test set-up errors is insufficient
Solution Approach 1:
The measurement process is segmented into multiple measurement series, each with a different number of rotational positions (M and N, where M and N are relatively prime). This segmentation allows the evaluation algorithm to separately analyze and separate test object errors from test set-up errors by examining the rotational symmetry characteristics at different resolution levels, thereby improving error separation capability without requiring a single overly complex measurement process
Solution Approach 2:
The method employs periodic rotational positioning of the test object at multiple series of equidistant rotational positions. By systematically varying the number of periodic positions (M and N) across different measurement series, the evaluation can identify patterns that correspond to test object errors versus test set-up errors, enhancing measurement precision through periodic sampling at different densities
2Measurement precision
If multiple measurement series with different numbers of rotational positions are used, then test object and test set-up errors can be separated, but the measurement time increases
Solution Approach 1:
Instead of using a single comprehensive measurement series with a large number of rotational positions that would be time-consuming, the method employs multiple partial measurement series with smaller, manageable numbers of rotational positions (M and N). These partial measurements collectively provide sufficient information for error separation while reducing the total measurement time compared to a single exhaustive measurement approach
Solution Approach 2:
The evaluation algorithm performs preliminary analysis during each measurement series to identify and characterize error patterns. By preliminarily separating test object errors from test set-up errors in each series, the method accumulates reliable error separation results across multiple series without requiring all measurements to be processed simultaneously, thereby managing measurement time efficiently
3Measurement precision
If rotation averaging method is applied, then test set-up errors are reduced, but rotationally symmetrical portions and wavinesses cannot be captured
Solution Approach 1:
The method deliberately introduces asymmetry in the number of rotational positions used in different measurement series (M and N are relatively prime, creating asymmetric sampling patterns). This asymmetric approach prevents the cancellation of rotationally symmetrical error components that occurs in conventional symmetric rotation averaging, thereby preserving information about rotationally symmetrical portions and wavinesses while still reducing test set-up errors
Solution Approach 2:
The method creates multiple copies of the measurement process with different numbers of rotational positions (M and N). By evaluating and comparing these copies, the algorithm can distinguish between true test object characteristics and measurement artifacts. The copying approach allows retention of rotationally symmetrical information that would otherwise be lost in single-series rotation averaging, as the pattern recognition across multiple copies preserves such features
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This method enables reliable and accurate characterization of the surface shape of optical elements, even those with complex, non-rotationally symmetrical shapes, within relatively short measurement times, thereby improving the precision and efficiency of surface testing.
Implementation Method 1
a measurement wave reflected by the surface to be examined is superimposed with a reference wave and the interference pattern generated in the process is captured
Data Source
AI summary
In a method for characterizing the surface shape, the following steps are carried out iteratively: (A) calculating a first figure based on first measurements; (B) subtracting the first figure from first measured values, to determine a first test set-up error; (C) using the first test set-up error for calculating a corrected first figure,; (D) subtracting the corrected first figure from second measured values, to determine a second test set-up error; (E) using the second test set-up error for calculating a corrected second figure; (F) using the corrected second figure for correcting the first test set-up error by subtracting the corrected second figure from the first measured values, to determine a corrected first test set-up error; (G) using the corrected first test set-up error for calculating a first figure corrected once again; and (H) comparing the result with a convergence criterion and optionally repeating steps (A) to (H).