Laser modulated scattering as a nondestructive evaluation tool for optical surfaces and thin film coatings Page: 4 of 11

                                
advantages of the LMS technique include its potential adaptability to lock-in imaging with focal array detectors
and its high sensitivity to small defects even with large pump / probe beam sizes.
This paper briefly describes the LMS technique, summarizes the preliminary results that serve as a feasibility
study, and discusses future applications of LMS to surface and subsurface defect inspection in optical materials.
2. Principle and model
The principle of laser modulated scattering from a defect is illustrated in Figure 1. For a typical microscopic tool
(such as optical microscopy), it is the DC scattering from the defect that is measured, as shown in Figure 1 (a). If a
pump laser is used to irradiate the defect, absorption at the defect and/or the host material will cause a localized
temperature rise and hence a number of photothermal effects, including a change in the scattering field of the
probe beam. By amplitude-modulating the pump beam, a modulated scattering field can be generated, as
illustrated in Figure 1(b).
The modulated scatter, or LMS, signal can be detected using lock-in techniques. Mapping of an optic can be
achieved by either scanning the sample or using a detector array. For the scanning case, the resolution is
determined by the size of the pump and/or the probe laser beam. When imaging using a focal array detector, the
pixel size of the image is the limiting factor for the spatial resolution.
Note that the spatial resolution should not be confused with the sensitivity of the technique for defect detection.
The latter depends on the magnitude of the signal relative to the background, not the physical size of the defect.
For microscopy based on LMS, the signal from a perfect surface is zero; therefore its sensitivity to local defects on
or underneath a super-polished surface can be extremely high.
Probe beam                               Pump beam
Reflected  Incident beam  I       Reflected
beam                              beam
ut tted                  '       lih  (AC)
(a) DC scattering         (b) Laser modulated scattering (LMS)
Figure 1. Illustration of the principle of laser modulated scattering (LMS): (a). Scattering (DC) from a defect;
(b). An amplitude-modulated pump laser beam is used to generate LMS.
The detection of light scattered by the laser-heated region is more informative than the DC scattering for laser
damage studies, as long as local-absorption induced thermal / thermo-mechanical response remains the dominant
damage mechanism. The variation of the refractive index due to laser heating typically is very small for optics
with low optical absorption. Therefore the LMS signal can be described theoretically using a perturbation method,
starting with a solution of the localized temperature rise caused by the laser heating.
Consider a Gaussian laser beam with a radius of a normally incident on the surface of the sample. Let us assume
the contribution of the defect absorption is equivalent to a surface absorption of the local area with absorption
coefficient a. The localized surface temperature T (t, r)is then given by formula [161
t
aa2    r T      Z            r2
T(t, r)=    2        T)f4(2  Ex   - (2+'     dz              (I)
k DT0 E(       1          p+)