Transcript Metrology
INC 681 Optical Metrology Moiré Techniques 24/09/05 Wiroj Sudatham Metrology Engineering INC 681 Optical Metrology Moiré Techniques Scope • Introduction to Moiré Metrology • Techniques Used in Moiré Metrology • Applications • Summary INC 681 Optical Metrology Introduction to Moiré Metrology Introduction Metrology : The science of weights and measures. Light : Particles Wave An electromagnetic periodic perturbation propagation in space at a constant velocity. INC 681 Optical Metrology Introduction to Moiré Metrology Historical Background 17th : Robert Hooke 1870s : Albert Abraham 1629-95 : Christian Huygens Michelson Michelson 19th : ThomasInterferometer Young later : James C. Maxwell INC 681 Optical Metrology Introduction to Moiré Metrology Moiré Effect and Interferometry • Superposition • Interference • Coherence Moiré Effect : any source of light can be used. Interferometry : base on mutual temporal coherence. INC 681 Optical Metrology Introduction to Moiré Metrology Analysis of The Moiré Pattern X n y cos / 2 x sin np y cos / 2 x sin mp k=12345… n 0, 1, 2... p p m 0, 1, 2... lp x 2 sin / 2 lp x m Y P Ronchi ruling INC 681 Optical Metrology Introduction to Moiré Metrology Moiré pattern response to grating’s deformations p p p Case1 : Shifted y cos / 2 x sin / 2 p np y cos / 2 x sin / 2 np p ( m n) p lp p x 2 sin / 2 2 sin / 2 INC 681 Optical Metrology Introduction to Moiré Metrology Moiré pattern response to grating’s deformations Case2 : Rotated y cos( / 2 ) x sin( / 2 ) np y cos / 2 x sin / 2 p np lp lp x 2 sin(( ) / 2) INC 681 Optical Metrology Introduction to Moiré Metrology Moiré pattern response to grating’s deformations Case3 : Beats Phenomenon I A 2 2 2 A A01 A02 2 A01 A02 cos( 1 2 ) 2 1 1 A A A 2 A01 A02 cos 2ct 2 1 y np2 y mp1 p1 kp2 2 2 01 2 02 1 1 l y p2 p1 INC 681 Optical Metrology Techniques Used in Moiré Metrology Techniques Used in Moiré Metrology Moiré Method Fringe quality improvement and Fringe readout techniques Extraction Information INC 681 Optical Metrology Techniques Used in Moiré Metrology Fringe Quality Improvement And Readout Techniques Grating’s Stripes Multiplication and Addition Multiplication The fringe result from multiplication of the transition functions of two grating and they occur when the two grating are superimposed. Stripes multiplication reduces the number of fringe with out any loss in the accuracy. INC 681 Optical Metrology Techniques Used in Moiré Metrology Fringe Quality Improvement And Readout Techniques Grating’s Stripes Multiplication and Addition Addition Collimated beam Collimated beam G1 G2 Object Stripes addition setup. INC 681 Optical Metrology Techniques Used in Moiré Metrology Fringe Quality Improvement And Readout Techniques Grating’s Stripes Multiplication and Addition 2 t1 ( x, y ) a a cos p Multiplication t ( x, y) t1t 2 x x t 2 ( x, y) a a cos 2 ( x) p Addition t ( x, y) t1 t 2 INC 681 Optical Metrology Techniques Used in Moiré Metrology Fringe Quality Improvement And Readout Techniques Spatial filtering Spatial filtering removes the high spatial frequency and leaves only the moiré pattern. Phase Shift Fringe Readout Method One of the fringes is move by 1/3 of its pitch. INC 681 Optical Metrology Techniques Used in Moiré Metrology Information Extraction Mapping f(x,y) Distorted Gratings general form: y f i ( x, y) np i 1, 2, 3.. n 0, 1 2... f i ( x, y) is the measured quantity Mapping y f ( x, y ) np y mp f ( x, y ) lp l m n A contour map of incremented by p INC 681 Optical Metrology Techniques Used in Moiré Metrology Information Extraction Mapping of Difference Two functions are difference : y f1 ( x, y) np y f 2 ( x, y) mp f1 ( x, y) f 2 ( x, y) lp This result is a contour of the difference between the two function which incremented by INC 681 Optical Metrology Techniques Used in Moiré Metrology Information Extraction Mapping The Sum x f 1 ( x, y ) p n x f 2 ( x, y ) p l l n m The sum of the finite fringe is the contour map: f1 ( x, y) f 2 ( x, y) mp INC 681 Optical Metrology Techniques Used in Moiré Metrology Information Extraction Multiplication by Factor y f ( x, y) np1 y mp2 p1 p2 y f ( x, y ) y l mn p1 p2 Beats pitch : 1 1 1 p p1 p 2 y Mf ( x, y ) lp where M p / p1 INC 681 Optical Metrology Techniques Used in Moiré Metrology Information Extraction Weighted Sums and Difference y f1 ( x, y) np1 y f 2 ( x, y) mp2 p p y f 1 ( x, y ) f 2 ( x, y ) lp p1 p2 INC 681 Optical Metrology Application Applications Shadow Moiré Collimated beam Observer Grating z Object x y Shadow moiré setup INC 681 Optical Metrology Application Applications Shadow Moiré y mp y h( x, y ) tan np shadow. parallel • Moiré pattern • Contour phase constant difference INC 681 Optical Metrology Application Applications Shadow Moiré y mp y h( x, y ) tan np where h( x, y ) tan 0 h( x, y ) tan (n m) p h( x, y ) lp cot INC 681 Optical Metrology Application Applications Moiré Analysis of Strain Observer f ( x, y ) f ( x x, y y ) distorted Measured surface INC 681 Optical Metrology Application Applications Moiré Analysis of Strain ( x, y ) np ( x, y y ) mp ( x, y y ) ( x, y ) lp ( x, y y) ( x, y) lp y y y INC 681 Optical Metrology Summary Moiré techniques Metrology • Introduction Light • Techniques • Applications Improvement Extraction Information Shadow moiré Metrology Etc. INC 681 Optical Metrology Reference Kjell J. Gasvik, (1995) JHON WILEY&SON 2nd, “OPTICAL METROLOGY”, 161-76. DR. ODED KAFRI and DR. ILANA GLATT, (1989) JHON WILEY&SON, “The Physics of Moiré Metrology”. Thanks น.อ. สหพงษ์ เครื อเพ็ชร รน. for a good advice.