OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 4 — Apr. 1, 2007
  • pp: 1156–1163

Theoretical and experimental investigation of the thermal resolution and dynamic range of CCD-based thermoreflectance imaging

Peter M. Mayer, Dietrich Lüerßen, Rajeev J. Ram, and Janice A. Hudgings  »View Author Affiliations

JOSA A, Vol. 24, Issue 4, pp. 1156-1163 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (353 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We demonstrate thermal imaging using a charge-coupled device (CCD) thermoreflectance lock-in technique that achieves a record temperature resolution of 18 mK , 44 dB below the nominal dynamic range of the camera (from 72 to 116 dB ) for 10 5 periods of measurement. We show that the quantization limit of the CCD camera does not set the lower bound on the precision of the technique. We present a theoretical description of the measurement technique, accounting for the effects of noise and nonideal analog-to-digital conversion, resulting in analytic expressions for the probability distribution function of the measured signals, and allowing for explicit calculation of resolution and error bars. The theory is tested against parametrically varied measurements and can be applied to other sampled lock-in measurements. We also experimentally demonstrate sub-quantization-limit imaging on a well-characterized model system, joule heating in a silicon resistor. The accuracy of the resistor thermoreflectance measurement is confirmed by comparing the results with those of a standard 3 ω measurement.

© 2007 Optical Society of America

OCIS Codes
(000.2170) General : Equipment and techniques
(040.1520) Detectors : CCD, charge-coupled device
(120.5700) Instrumentation, measurement, and metrology : Reflection
(120.6780) Instrumentation, measurement, and metrology : Temperature

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: September 11, 2006
Revised Manuscript: November 7, 2006
Manuscript Accepted: November 10, 2006
Published: March 14, 2007

Peter M. Mayer, Dietrich Lüerßen, Rajeev J. Ram, and Janice A. Hudgings, "Theoretical and experimental investigation of the thermal resolution and dynamic range of CCD-based thermoreflectance imaging," J. Opt. Soc. Am. A 24, 1156-1163 (2007)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. Marek and Y. E. Strausser, "Correlation of thermal-wave imaging to other analysis methods," Appl. Phys. Lett. 44, 1152-1154 (1984). [CrossRef]
  2. O. Breitenstein, M. Langenkamp, F. Altmann, D. Katzer, A. Lindner, and H. Eggers, "Microscopic lock-in thermography investigation of leakage sites in integrated circuits," Rev. Sci. Instrum. 71, 4155-4160 (2000). [CrossRef]
  3. K. Luo, Z. Shi, J. Varesi, and A. Majumdar, "Sensor nanofabrication, performance, and conduction mechanisms in scanning thermal microscopy," J. Vac. Sci. Technol. B 15, 349-360 (1997). [CrossRef]
  4. M. Cardona, Modulation Spectroscopy, Solid-State Physics, Supplement 11 (Academic, 1969).
  5. D. Cahill, K. Goodson, and A. Majumdar, "Thermometry and thermal transport in micro/nanoscale solid-state devices and structures," J. Heat Transfer 124, 223-241 (2002). [CrossRef]
  6. J. Christofferson and A. Shakouri, "Thermoreflectance based thermal microscope," Rev. Sci. Instrum. 76, 24903-24909 (2005). [CrossRef]
  7. S. Dilhaire, S. Grauby, and W. Claeys, "Calibration procedure for temperature measurements by thermoreflectance under high magnification conditions," Appl. Phys. Lett. 84, 822-824 (2004). [CrossRef]
  8. S. Grauby, B. C. Forget, S. Hole, and D. Fournier, "High resolution photothermal imaging of high frequency phenomena using a visible charge coupled device camera associated with a multichannel lock-in scheme," Rev. Sci. Instrum. 70, 3603-3608 (1999). [CrossRef]
  9. C. Filloy, G. Tessier, S. Hole, G. Jerosolimski, and D. Fournier, "The contribution of thermoreflectance to high resolution thermal mapping," Sens. Rev. 23, 35-39 (2003). [CrossRef]
  10. M. Fujinami, K. Toya, and T. Sawada, "Development of photothermal near-field scanning optical microscope photothermal near-field scanning optical microscope," Rev. Sci. Instrum. 74, 621-623 (2003). [CrossRef]
  11. G. Tessier, S. Hole, and D. Fournier, "Ultraviolet illumination thermoreflectance for the temperature mapping of integrated circuits," Opt. Lett. 28, 875-877 (2003). [CrossRef] [PubMed]
  12. G. Tessier, S. Hole, S. Grauby, and D. Fournier, "Quantitative thermal imaging by thermoreflectance using a CCD array," Presented at THERMINIC 2000, International Workshop No. 6, Budapest, September 24, 2000.
  13. S. Grauby, S. Dilhaire, S. Jorez, and W. Claeys, "Imaging setup for temperature, topography, and surface displacement measurements of microelectronic devices," Rev. Sci. Instrum. 74, 645-647 (2003). [CrossRef]
  14. C.-H. Ho, H.-W. Lee, and Z.-H. Cheng, "Practical thermoreflectance design for optical characterization of layer semiconductors," Rev. Sci. Instrum. 75, 1098-1102 (2004). [CrossRef]
  15. J. Christofferson and A. Shakouri, "Camera for thermal imaging of semiconductor devices based on thermoreflectance," in Proceedings of the 20th Annual IEEE Semiconductor Thermal Measurement and Management Symposium (IEEE, 2004), pp. 87-91.
  16. J. Philip and K. Carlsson, "Theoretical investigation of the signal-to-noise ratio in fluorescence lifetime imaging," J. Opt. Soc. Am. A 20, 368-379 (2003). [CrossRef]
  17. E. Balestrieri, P. Daponte, and S. Rapuano, "A state of the art on ADC error compensation methods," IEEE Trans. Instrum. Meas. 54, 1-8 (2005). [CrossRef]
  18. P. Carbone, "Quantitative criteria for the design of dither-based quantizing systems," IEEE Trans. Instrum. Meas. 46, 656-659 (1997). [CrossRef]
  19. P. Carbone and D. Petri, "Effect of additive dither on the resolution of ideal quantizers," IEEE Trans. Instrum. Meas. 43, 389-396 (1994). [CrossRef]
  20. L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, "Stochastic resonance," Rev. Mod. Phys. 70, 223-287 (1998). [CrossRef]
  21. R. A. Wannamaker, S. P. Lipshitz, J. Vanderkooy, and J. N. Wright, "A theory of nonsubtractive dither," IEEE Trans. Signal Process. 48, 499-516 (2000). [CrossRef]
  22. J. Potzick, "Noise averaging and measurement resolution (or "A little noise is a good thing")," Rev. Sci. Instrum. 70, 2038-2040 (1999). [CrossRef]
  23. D. Luerssen, J. A. Hudgings, P. M. Mayer, and R. J. Ram, "Nanoscale thermoreflectance with 10mK temperature resolution using stochastic resonance," in Proceedings of the 21st Annual IEEE Semiconductor Thermal Measurement and Management Symposium (IEEE, 2005), pp. 253-258.
  24. S. Inoué and K. R. Spring, Video Microscopy: The Fundamentals, 2nd ed. (Plenum, 1997). [CrossRef]
  25. G. Busse, D. Wu, and W. Karpen, "Thermal wave imaging with phase sensitive modulated thermography," J. Appl. Phys. 71, 3962-3965 (1992). [CrossRef]
  26. O. Breitenstein and M. Langenkamp, Lock-in Thermography: Basics and use for Functional Diagnostics of Electronic Components, Springer Series in Advanced Microelectronics (Springer, 2003).
  27. W. M. Hubbard, "Approximation of a Poisson distribution by a Gaussian distribution," Proc. IEEE 58, 1374-1375 (1970). [CrossRef]
  28. J. Janesick, "CCD transfer method—standard for absolute performance of CCDs and digital CCD camera systems," Proc. SPIE 3019, 70-102 (1997). [CrossRef]
  29. Y. Reibel, M. Jung, M. Bouhifd, B. Cunin, and C. Draman, "CCD or CMOS camera noise characterization," Eur. Phys. J.: Appl. Phys. 21, 75-80 (2003). [CrossRef]
  30. A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing, Prentice Hall Signal Processing Series, 2nd ed. (Prentice Hall, 1999).
  31. C. F. Coombs, Electronic Instrument Handbook, 3rd ed. (McGraw-Hill, 2000).
  32. J. C. Mullikin, L. J. V. Vliet, H. Netten, F. R. Boddeke, G. v. d. Feltz, and I. T. Young, "Methods for CCD camera characterization," Proc. SPIE 2173, 73-84 (1994).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited