n 令 E = ∑ ( yi − Axi − B) 2 i=0 ( ) ( ) ∂E n n = 2 ∑ y − Ax − B (− x ) = 0 ∂E = 2 ∑ y − Ax − B (− 1) = 0 ∂A i i ∂B i i i=0 i=0 聯立 易 數 率 理 來AOI Lecture Precision Metrology Lab.
Minimum Distance Method 念 料 料 度 令 ( y − y0 ) cosθ − ( x − xm ) sin θ = 0 θ 參數 xm 料 令 列 2 S= ∑ d i n ∑ i 0 ( 2 = n ( y − y ) cosθ − ( x − x ) sin θ i m ) i =1 i =1 ∂S =0 ∂S =0 ∂y 0 ∂θ 1 n y = ∑ yi = y m 料 0 n i=1 1 ⎛ 2I ⎞ θ = tan −1⎜ xy ⎟ ⎜ Ix − Iy ⎟ 2 ⎝ ⎠ n n I xy = ∑ ( xi − x m )( y i − y m ) I x = ∑ ( xi − x m ) n 2 I y = ∑ ( yi − y m ) 2 i =1 i =1 i =1AOI Lecture Precision Metrology Lab.
Least Squares Circle 度 輪廓 狀 離 料 x2 + y2 + Ax+ By+C = 0 S : S = ∑δi2 =∑(xi2 + yi2 + Axi + Byi + C)2 A B C S ∂S ∂S = ∑2(xi2 + yi2 + Axi + Byi + C)(xi ) = 0 = ∑ 2( xi2 + yi2 + Axi + Byi + C)( yi ) = 0 ∂A ∂B ∂S = ∑2( xi2 + yi2 + Axi + Byi + C)(1) = 0 ∂C ⎡ ∑ xi2 ∑ x y ∑ x ⎤ ⎡ A⎤ ⎡− ∑ x ( x + y )⎤ i i i i 2 i 2 i ⎢ ⎥ ⎢ ⎥ 聯立 ⎢∑ xi yi ∑ y ∑ y ⎥ ⎢ B ⎥ = ⎢− ∑ y ( x + y ) ⎥ 2 ⎢ ⎥ i i i i 2 i 2 ⎢ ∑ xi ∑ y ∑ ⎦⎣ ⎦ ⎣ 1 ⎥ ⎢C ⎥ ⎢ − ∑ ( x + y ) ⎥ 2 2 ⎣ i ⎦ i i ( X 0 , Y0 ) = ⎛ − A ,− B ⎞ ⎜ R= (A 2 + B 2 − 4C ) ⎝ 2 2⎠ 2AOI Lecture Precision Metrology Lab.
- Position accuracy of reference pin - Position accuracy for reference frame - Each parts pitch - Shape accuracy p y - Radius of curvature - Slot width and tolerance etcAOI Lecture Precision Metrology Lab.
Point Laser Triangulation Principle of measurement: A semiconductor laser beam is reflected off the target surface and passes through a custom designed receiver lens system. The beam is focused on a CCD sensing array. f d i The CCD detects the peak value of the light quantity distribution of the beam spot. The CCD pixels spot (individual CCD sensing elements) within the area of the beam spot are used to determine the precise target position. Range R l ti R Resolution S d Speed 10mm 1µm 30mm/sec 30mm 3µm 30mm/secAOI Lecture Precision Metrology Lab.
雷 Panasonic P i RVSIAOI Lecture Precision Metrology Lab.
Autofocusing Probe Photodiode IC Cylindrical Lens y Laser Diode Grating Polarization Beam Splitter 1/4 λ Plate Arm Spring Objective Lens Voice Coil Motor DiscAOI Lecture Precision Metrology Lab.
Principle Of Autofocus Sensor High precision measurement with 1 µm laser spot by means of a focus detector with nanometer resolution and a glass scale with an absolute accuracy of 0.025 µmAOI Lecture Precision Metrology Lab.
Astigmatic Method Y Plane1 Plane3 Plane2 Z X Schematic of the Astigmatic methodAOI Lecture Precision Metrology Lab.
Analog S-curve Signal S curve Plane1 + V + Plane2 0 µm 0 - 30 µm Plane3 -AOI Lecture Precision Metrology Lab.
Auto focus Auto-focus Theory Servo-FES FES Astigmatic g Autofocus Method Method Disp. Disp. Disp 30 um 1500 umAOI Lecture Precision Metrology Lab.
S-curves for various materials S-Curve vs. Material 3000 2000 Mirror (Al) FES (m V) 1000 Mirror (Hg) 0 CD S -1000 Si -2000 -3000 20 30 40 50 0 60 70 0 80 Position (µm)AOI Lecture Precision Metrology Lab.
Auto focusing characteristics for various materials 1200 AutoFocus vs. Material 800 Mirror Servo-FE (mV) 400 (Al) Mirror ES (Hg) 0 CD -400 Si S -800 -1200 0 200 400 600 800 1000 1200 1400 Position (µm)AOI Lecture Precision Metrology Lab.
Experiment Coin Shading g 3D D t DataAOI Lecture Precision Metrology Lab.
Experiment p Etching Profile g Profile Height (um) Position ( ) P iti (um)AOI Lecture Precision Metrology Lab.
Multi-wavelength Focus Principle of measurement: White light is directed by a beam splitter through a spectral aberration lens onto the surface. The lens splits the light into different wavelengths and at any point on the surface only a certain wavelength will be in focus. Light is reflected from the surface to a p hole g pin which permits only the wavelength in focus to pass through. A spectrometer deflects the light onto a CCD sensor to interpolate spatial position of the data point. p Range Resolution Speed 3mm 100nm 30mm/sec 1mm 30nm 30mm/sec 300µm 10nm 30mm/secAOI Lecture Precision Metrology Lab.
Principle of White Light Confocal SensorAOI Lecture Precision Metrology Lab.
Application on Semiconductors Quality control on coplanarity, warpage, laser marking depth, etc. g p , 00 2.00 µm] 10^4 0.000AOI Lecture Precision Metrology Lab.
Laser Confocal Displacement Keyence LT-9000 LT 9000 How It Works : Z-axis: A tuning fork is combined with the confocal principle to obtain high accuracy measurement. X-axis: An oscillating unit i ill i i creates a wide scan area. This allows increased measurement stabilityAOI Lecture Precision Metrology Lab.
Stereo Microscope ( ) p (1) Interferometer I t f tAOI Lecture Precision Metrology Lab.
Profile Interferometry y • Non-Destructive Measurement • 3D Surface Measurement • Multiple Field of View Lens • N Nanometer Level Resolution and Large t L l R l ti dL Measuring range • Fast Measurement • E Ease of Use fU • Convenient Loading and Setup g pAOI Lecture Precision Metrology Lab.
Holographic Interferometry Measurement principle Digital Holographic Microscopy (DHM) is the generation of computer images of a sample using holographic techniques. A hologram results from the interference between the object wave diffracted by a sample and magnified by a microscope objective, and a reference wave. Using laser illumination, the small angle between the waves exhibits fringes that carry the phase and amplitude information in a single image - the hologram - which is captured on a digital camera. The appropriate processing of a single hologram retrieves the complete wavefront and the numerical propagation permits the focusing in different planes. Digital holography is capable of resolving differences corresponding to height differences under the nanometer.AOI Lecture Precision Metrology Lab.