Enhanced evanescent prism coupling systems and methods for characterizing stress in chemically strengthened curved parts

A method of determining at least one of a refractive index profile and at least one stress-related characteristic of a curved chemically strengthened (CS) substrate using an evanescent prism coupling system having an adjustable focus, comprising:

• a) calibrating the evanescent prism coupling system by adjusting the adjustable focus to a first focus that forms an in-focus calibration mode spectrum image of a reference CS substrate to establish a calibrated system for measuring the reference CS substrate;
• b) using the calibrated system, forming an in-focus mode spectrum image for the curved CS substrate by adjusting the adjustable focus to a second focus due to a focus shift caused by using the curved CS substrate in the calibrated system for measuring a flat CS substrate, wherein using the calibrated system further comprises:
• optically coupling measurement light beam into and out of the curved CS substrate using a coupling prism, the coupling prism interfaced with a curved surface of the CS substrate to define a coupling interface;
• and
• transmitting the measurement through the coupling prism along an axis through a detector optical system having the second focus to a digital detector where the in-focus mode spectrum image is formed;
• c) determining a raw value of at least one stress-related characteristic of the curved CS substrate based on the in-focus mode spectrum image for the curved CS substrate using a corresponding at least one calculation for the at least one stress-related characteristic for the flat CS substrate;
• and
• d) adjusting the raw value of the at least one stress-related characteristic to obtain a corrected value by multiplying the raw value by a correction factor based on a change in the adjustable focus from the first focus for the flat CS substrate to the second focus for the curved CS substrate.

A method of determining at least one stress-related characteristic for a chemically strengthened (CS) substrate having a curved surface and an adjacent near-surface waveguide adjacent the curved surface, comprising:

• optically coupling a measurement light beam into and out of the near-surface waveguide using a coupling prism, the coupling prism interfaced with the curved surface of the CS substrate to define a coupling interface;
• transmitting the measurement light beam coupled out of the near-surface waveguide through the coupling prism along an axis through a detector optical system to a digital detector;
• digitally capturing transverse magnetic (TM) and transverse electric (TE) mode spectra of the CS substrate using an evanescent prism coupling system to couple measurement light into and out of the near-surface waveguide through the coupling prism of the evanescent prism coupling system having a prism refractive index np and defining coupling interface with the CS substrate to form a digital mode spectrum image with the digital detector, the evanescent prism coupling system having a system calibration comprising a system calibration parameter Kf for measuring flat CS substrates, wherein the TM and TE mode spectra comprise respective TM and TE mode lines having a corresponding effective index difference neff, the digitally captured TM and TE mode spectra are measured with the evanescent prism coupling system having an incidence angle α of a measurement light beam incident the coupling prism, l is a first axial distance between a detector optical system;
• establishing a calibration correction representative of a difference in the digitally captured TM and TE mode spectra as compared to a reference TM and TE mode spectra for a reference CS substrate, wherein the establishing of the calibration correction comprises calculating Δneff=Kd·Δx where Kd comprises a dynamic calibration parameter for the curved CS substrate, the dynamic calibration parameter Kd is calculated as:
• where P is given by P=[Kf L]−1 and Q is given by
• K
• d
• =
• PQ
• n
• p
• ⁢
• n
• p
• 2
• -
• n
• eff
• 2
• where P is given by P=[Kf L]−1 and Q is given by
• Q
• =
• 2
• ⁢
• l
• ⁢
• n
• p
• γ
• ⁢
• R
• ⁢
• cos
• ⁢
• α
• ,
• where γ is a system calibration parameter for measuring curved CS substrates having a local radius of curvature R at the coupling interface and;
• and
• processing the digitally captured TM and TE mode spectrum using the dynamic calibration parameter to determine the at least one stress-related characteristic.