# Presentation: 145452

## Valeriy V. Yashchuk,a) Wayne R. McKinney,a) and Peter Z. Takacs b) 

a) Lawrence Berkeley National Laboratory, Berkeley, California, 94720
b) Brookhaven National Laboratory, Upton, New York, 11973 

*a)** Lawrence Berkeley National Laboratory, Berkeley, California, 94720*
*b)** Brookhaven National Laboratory, Upton, New York, 11973*

- _vvyashchuk@lbl.gov_

**Binary pseudo-random grating ****as a standard test surface ****for measurement of modulation transfer functions of interferometric microscopes**

*SPIE Optics and Photonics 2007*
*“**Advances in Metrology for X-Ray and EUV Optics II”*
*San Diego, August 30, 2007*

*Proceedings of SPIE 6704-7*

## Outline

*Power spectral density (PSD) from surface roughness data*
*Reliable 2D PSD measurements require correction for instrumental **MTF** *
*Step-height standard and its disadvantages*
*Binary Pseudo-random (BPR) Grating for MTF measurements*
*Theoretical introduction: What is a BPR sequence?*
*What are the BPR sequences good for? *
*BPR grating as a standard test surface *
*Application of a BPR grating to measure MTF of the Micromap**TM**-570*
* *
*Conclusions*

**Outline**

## “One number” statistical 

***surface metrology***

***For all these cases the roughness value is the same!  ***
***The two-dimensional sketches show the need for at least two parameters. One is vertical (roughness) and one is horizontal (wavelength).***

*Roughness (rms):*

**Notes:**
Say here about necessity to account a correlation between the points. 
One way is via a correlation function, another is a spectral consideration. 

## Power Spectral Density (PSD) based

*The roughness value is the same. **But the PSD spectra are different!*

*Roughness (rms):*

*PSD based metrology permits measurement of instrumental modulation transfer function (MTF)*

***Power Spectral Density (PSD) based***
***surface metrology***

**Notes:**
Gene: OK, Ok. But Val – I think that you should somewhere point out that the PSD is not only a mathematical device for characterizing transverse and vertical character of topography, but also – for smooth surfaces -- the angular spectrum of scattering. 	Speckle and all! 

## PSD measurements 

- 1 V. V. Yashchuk, A. D. Franck, S. C. Irick, M. R. Howells, A. A. MacDowell, W. R. McKinney, *Two dimensional power spectral density measurements of X-ray optics with the Micromap interferometric microscope,* SPIE Symposium on Optical Metrology 2005, part of LASER2005, World of Photonics , SPIE Proceedings 5858, pp. 58580A-1-12 (Munich, Germany, 12-17 June 2005).
- 2 V. V. Yashchuk, E. M. Gullikson, M. R. Howells, S. C. Irick, A. A. MacDowell, W. R. McKinney, F. Salmassi, T. Warwick, J. P. Metz, and    T. W. Tonnessen, *Surface Roughness of Stainless Steel Mirrors for Focusing Soft X-rays, *Applied Optics 45(20), OT-65462 (2006).

***Reliable PSD  measurement requires correction for the instrument MTF.***
*** ******Standard test surfaces and MTF calibration procedures must be developed.***

***PSD measurements ***
***with the real instruments***

**Notes:**
A random fractal has no intrinsic roughness. The finite roughness is apparent rather 
than real since it is a result of bandwidth limits in the measurement process. 

Demonstrate also a limitation of 1D PSD and need for 2D PSD. 

The point is that a correct extrapolation requires first to perform all corrections... and correct (2D) presentation. 
By the way do you have any idea how one could extrapolate a 2D PSD spectrum say for using in estimation similar to one depicted with viewgraph #10 (new version)?

## Step-height standard

***Step-height standard for surface-profiler calibration, SPIE Proceedings 1995, 235-44 (1993).***

***Step-height standard***

***Disadvantages:***
**             *****intrinsic PSD spectrum and, therefore, low sensitivity to the higher spatial frequency distortion;***
***  ******necessity to preprocess data to filter out  PSD variations at higher spatial frequencies;***
***  ******strong dependence of calibration on position of the step in the instrumental field of view.***

## Binary Pseudo-random (BPR) sequences 

***Introduction to***
***Binary Pseudo-random (BPR) sequences****** ***

**1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0,0,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,1,0,0,0,0,0,1,1,1,1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,1,0,1,1,1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,1,1,1,1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0,1,1,0,1,0,1,1,1,1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,1,0,1,1,1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,1,1,1,0,1,1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,1,1,1,0,0,1,0,1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0,1,1,1,1,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,1,0,0,0,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0,0,0,0,0,1,1,1,0,1,1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0,0,1,0,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0,1,1,0,1,1,1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0,0,0,1,0,0,0,1,1,1,1,1,1,0,0,1,1,0,1,1,1,0,0,1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0**

***BPR sequence****** ******with 1023 elements***** **
*for n=10 with recursion coefficient M=45 **a)*

**sequence correlation function:**** **

**‘****deconvolution’ sequence:**** **

**δ****-function-like correlation function: **

** ****a)**** D. D. Koleske, and S. J. Sibener, *****Generation of pseudorandom sequence for use  in cross-correlation modulation, ***
***                                                           *****Rev. Sci. Instrum. 63(8), 3852-3855 (1992).**

***First 100 elements of the ******BPR***** *****sequence of total 1023 elements****** ***

**The best *****random***** sequences are mathematically strongly *****deterministic*****!**

## Binary Pseudo-random Chopping in a 

- V. V. Yashchuk, B. N. Ashkinadzi, M. N. Groshev, V. F. Ezhov, T. A. Isaev, V.A.Knyazkov, G. B. Krygin, V. L. Ryabov, *Cross-Correlation Time-of-Flight Spectrometer of Gas-Dynamic Molecular Beams,* Instruments and Experimental Techniques, 40(4), 501 (1997).

***Binary Pseudo-random Chopping in a ***
***Time-of-flight Spectrometer***

***pseudo-random ******chopping***
***in order to increase duty cycle***

**detector**

**atomic beam source**

## Binary Pseudo-random Grating as a 

***Binary Pseudo-random Grating as a ***
***Standard Test Surface for MTF measurement***

***First 200 elements of the BPR sequence of total 4095 elements ***

***  ******A prototype BPR grating test surface was etched into a silicon substrate using a conventional lithographical process.****** ***
***  ******The grating consists of ***

**     *****4095****** elements; ***
***     ******2.5 μm ******groove width; ***
***     ******174 nm****** ******effective****** depth***
*** ******It is good for 2.5******× objective with pixel size of ******3.9 μm***** **

**The PSD spectrum of the BPRG is mathematically strongly *****deterministic*****!**

## BPRG test surface (2.5 μm pitch) 

***Micromap-570 measurement ******with***
***BPRG test surface (2.5 μm pitch) ***

**50x objective  **(0.26 μm pixel size)** **

## BPRG test surface (2.5 μm pitch) 

**50x objective  **(0.26 μm pixel size)** **

***The etch depth was measured to be***
***	******~700 nm****** with an AFM  and***
***	****** ******174 nm****** with the Micromap******TM******-570. ***
***The discrepancy (******λ******=520 nm)****** is due to the uncertainty of  the phase-retrieval algorithm of micro-roughness instruments. ***

***Micromap-570 measurement ******with***
***BPRG test surface (2.5 μm pitch) ***

## BPRG test surface (2.5 μm pitch) 

**2.5x objective   **(3.9 μm pixel size)

***Micromap-570 measurement ******with***
***BPRG test surface (2.5 μm pitch) ***

## BPRG test surface (2.5 μm pitch) 

**50x objective     **(0.26 μm pixel size)

**2.5x objective    **(3.9 μm pixel size)

***Micromap******TM******-570 measurement ******with***
***BPRG test surface (2.5 ******μm pitch)****** ***

## BPRG test surface (2.5 μm pitch) 

***Micromap******TM******-570 measurement ******with***
***BPRG test surface (2.5 ******μm pitch)****** ***

***The difference in PSD presentation is to be described with the MTF***

**Calculated with 3.9 ****μm sampling**

**Measured with 2.5****×**** objective**

## PSD spectrum of BPRG test surface 

***PSD spectrum of BPRG test surface***** **
***of 4095 elements with 2.5-************m pitch***

***The simulation and measurement fields of view correspond to the 480 pixel row length in the Micromap.***** **
***Vertical offset of the lower spectrum is made for clarity.***

***measured with the MicromapTM-570 microscope with 2.5x objective***

***The difference of the PSD spectra is due to the instrumental MTF***

***model simulation resampled onto a 3.92 μm grid***

## MTF correction with BPRG test surface 

***MTF correction ******with BPRG test surface***** **
***of 4095 elements with 2.5-************m pitch***

**********) ******E. L. Church, P. Z. Takacs, Effects of optical transfer function in surface-profile measurements, ***
***Proceedings of SPIE, 1164 (1989), 46-59.***

***measured with the MicromapTM-570 microscope with 2.5x objective***

***The theoretical PSD spectrum is corrected to account for the instrumental MTF due to:*******)***

*** ******effective pixel size***

*** ******diffraction limited objective***

***model simulation resampled onto a 3.92 μm grid***

## ALS OML PSD Software 

***ALS OML PSD Software ***
***for Micromap******TM******-570***

***Developed in collaboration with Thomas Zeschke (BESSY, Germany)****** ***

## ALS OML PSD Software 

***ALS OML PSD Software ***
***for Micromap******TM******-570***

*Height distribution measured with Macromap-570**** ***

## ALS OML PSD Software 

*Correction of CCD read-out asymmetry*

***ALS OML PSD Software ***
***for Micromap******TM******-570***

## ALS OML PSD Software

***ALS OML PSD Software***

*Correction of finite pixel size**** ***

## ALS OML PSD Software 

*Correction of finite pixel size: **Nyquist frequency is changed**** ***

***ALS OML PSD Software ***
***for Micromap******TM******-570***

## ALS OML PSD Software 

*Correction of* *incoherent transfer function of a diffraction-limited objective**** ***

***J. W. Goodman, Introduction to Fourier Optics, third edition (Roberts & Company Publishers, Englewood, 2005).***
***E. L. Church, P. Z. Takacs, Effects of optical transfer function in surface-profile measurements, Proceedings of SPIE, 1164 (1989), 46-59.***

***ALS OML PSD Software ***
***for Micromap******TM******-570***

## ALS OML PSD Software 

*Correction of* *incoherent transfer function of a diffraction-limited objective**** ***

***ALS OML PSD Software ***
***for Micromap******TM******-570***

## ALS OML PSD Software 

*Correction of* *incoherent transfer function of a diffraction-limited objective *

***J. W. Goodman, Introduction to Fourier Optics, third edition (Roberts & Company Publishers, Englewood, 2005).***
***E. L. Church, P. Z. Takacs, Effects of optical transfer function in surface-profile measurements, Proceedings of SPIE, 1164 (1989), 46-59.***

***ALS OML PSD Software ***
***for Micromap******TM******-570***

##  Conclusions

* **Efficiency of Binary Pseudorandom Grating (BPRG) based method for MTF measurements has been demonstrated. *
* **Consistence of the BPRG calibration and semi-empirical calibration based on extrapolation of measurements with different objectives has be shown.*
*The developed PSD algorithm allows for correction of the CCD read-out asymmetry and accounting for the MTF due to finite pixel*** ***size and diffraction-limited objective.*
*PSD analysis was successfully applied to the MicroMap-570 interferometric microscope measurements of surface roughness.*
* ****Next:****   MTF correction based on PSD measurements  *
*                **with 2D binary pseudorandom test surface;*
*	**  **Binary pseudorandom test surface based standard*

## Acknowledgements

*The authors are grateful to *
*	**	****John Warren, ***
***	******	******	******Don Elliott, ***
***	******	******	******	******Abdel Isakovic, and ***
***	******	******	******	******	******Rolf Beuttenmuller**** *
*at Brookhaven National Lab for fabrication of the BPRG test surface, and *
*	**	**	****Farhad Salmassi**** *
*at the Lawrence Berkeley Lab for measurements with an atomic force microscope.*** **

***Disclaimer***
*Certain commercial equipment, instruments, or materials are identified in this document. Such identification does not imply recommendation or endorsement by the US Department of Energy, LBNL or ALS nor does it imply that the products identified are necessarily the best available for the purpose.*

***The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, Material Science Division, of the U.S. Department  of Energy under Contract No. DE-AC02-05CH11231 at Lawrence Berkeley National Laboratory. This work has been authored in part by Brookhaven Science Associates, LLC under Contract No. DE-AC02-98CH10886 with the U.S. Department of Energy.***** **

**Notes:**
Is the sun rising or setting on LBL. Tell me quickly!
Yes, Yes, Yes... But what ‘yes’ means, you know better!!! Ha-ha-ha!
Remember Einstein’s dictum: Things should be made as simple as possible, but no simpler!
This is probably why he did not accept quantum theory: it is too simple comparing with his general relativity!
But speaking seriously, Gene, may I call you my Teacher in metrology? 
Thank you, thank you, thank you so much!!!

## THANKS!

**L****AWRENCE**** B****ERKELEY**** N****ATIONAL**** L****ABORATORY**

**O****PTICAL**** M****ETROLOGY**** L****ABORATORY**
**E****XPERIMENTAL**** S****YSTEMS**** G****ROUP **
**A****DVANCED**** L****IGHT**** S****OURCE**

*June 16, 2005*

**THANKS!**