Previously we showed that the “bootstrap method,” a well-known statistical technique, can be used to automatically compute error bars in ultrashort pulse measurements using frequency-resolved optical gating (FROG) without the need for additional measurements or traditional error analysis. Here we extend the bootstrap method to pulse measurement in the presence of ambiguities, where traditional error bars would give misleading information. As a result, we provide a new approach to displaying this uncertainty, which nicely reveals the richness of information available (or perhaps unavailable) in a FROG trace (or other measurement) in the presence of ambiguities.

© 2003 Optical Society of America

1. R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic Publishers, Boston, 2002). [CrossRef]
2. Jung-Ho Chung and Andrew M. Weiner, �??Ambiguity of Ultrashort Pulse Shapes Retrieved from the Intensity Autocorrelation and the Power Spectrum,�?? J. Special Top. Quantum Electron. 7, 656-666 (2001). [CrossRef]
3. Y. M. Bruck and L. G. Sodin, �??On the ambiguity of the image reconstruction problem,�?? Opt. Commun. 30, 304�??308 (1979). [CrossRef]
4. Z. Wang, E. Zeek, R. Trebino, P. Kvam, �??Determining error bars in measurements of ultrashort laser pulses,�?? J. Opt. Soc. Am B 20, 2400-2405 (2003). [CrossRef]
5. R. P. Millane, �??Phase retrieval in crystallography and optics,�?? J. Opt.Soc. Am. A. 7, 394�??411 (1990). [CrossRef]
6. A. Walther, �??The question of phase retrieval in optics,�?? Opt. Acta. 10, 1�??49 (1963). [CrossRef]
7. Stark, H., ed. Image Recovery: Theory and Application. (Academic Press, Orlando, 1987).
8. Brad. Efron and R. J. Tibshirani, An Introduction to the Bootstrap (Chapman & Hall/CRC, Boca Raton, 1993).
9. C. Davison and D. V. Hinkley, Bootstrap Methods and Their Application (Cambridge University Press, Cambridge, 1997).
10. D. Keusters, H.S. Tan, P. O�??Shea, E. Zeek, R. Trebino, W. S.Warren, �??Relative-Phase Ambiguities in Measurements of Ultrashort Pulses with Well-Separated Multiple Frequency Components,�?? J. Opt. Soc. Am B 20, 2226-2237 (2003). [CrossRef]

J. Opt. Soc. Am B

• Z. Wang, E. Zeek, R. Trebino, P. Kvam, �??Determining error bars in measurements of ultrashort laser pulses,�?? J. Opt. Soc. Am B 20, 2400-2405 (2003). [CrossRef]
• D. Keusters, H.S. Tan, P. O�??Shea, E. Zeek, R. Trebino, W. S.Warren, �??Relative-Phase Ambiguities in Measurements of Ultrashort Pulses with Well-Separated Multiple Frequency Components,�?? J. Opt. Soc. Am B 20, 2226-2237 (2003). [CrossRef]

J. Opt.Soc. Am. A.

• R. P. Millane, �??Phase retrieval in crystallography and optics,�?? J. Opt.Soc. Am. A. 7, 394�??411 (1990). [CrossRef]

J. Special Top. Quantum Electron.

• Jung-Ho Chung and Andrew M. Weiner, �??Ambiguity of Ultrashort Pulse Shapes Retrieved from the Intensity Autocorrelation and the Power Spectrum,�?? J. Special Top. Quantum Electron. 7, 656-666 (2001). [CrossRef]

Opt. Acta.

• A. Walther, �??The question of phase retrieval in optics,�?? Opt. Acta. 10, 1�??49 (1963). [CrossRef]

Opt. Commun.

• Y. M. Bruck and L. G. Sodin, �??On the ambiguity of the image reconstruction problem,�?? Opt. Commun. 30, 304�??308 (1979). [CrossRef]

Other

• R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic Publishers, Boston, 2002). [CrossRef]
• Stark, H., ed. Image Recovery: Theory and Application. (Academic Press, Orlando, 1987).
• Brad. Efron and R. J. Tibshirani, An Introduction to the Bootstrap (Chapman & Hall/CRC, Boca Raton, 1993).
• C. Davison and D. V. Hinkley, Bootstrap Methods and Their Application (Cambridge University Press, Cambridge, 1997).

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