Abstract

Speckle patterns produced by a disordered medium or a multimode fiber can be used as a fingerprint to uniquely identify the input light frequency. Reconstruction of a probe spectrum from the speckle pattern has enabled the realization of compact, low-cost, and high-resolution spectrometers. Here we investigate the effects of experimental noise on the accuracy of the reconstructed spectra. We compare the accuracy of a speckle-based spectrometer to a traditional grating-based spectrometer as a function of the probe signal intensity and bandwidth. We find that the speckle-based spectrometers provide comparable performance to a grating-based spectrometer when measuring intense or narrowband probe signals, whereas the accuracy degrades in the measurement of weak or broadband signals. These results are important to identify the applications that would most benefit from this new class of spectrometer.

© 2014 Optical Society of America

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References

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2013 (2)

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7, 1–6 (2013).

B. Redding, S. M. Popoff, and H. Cao, “All-fiber spectrometer based on speckle pattern reconstruction,” Opt. Express 21, 6584–6600 (2013).
[CrossRef]

2012 (1)

2010 (2)

2003 (1)

1976 (1)

1949 (1)

Adibi, A.

Brady, D.

Cao, H.

Dogariu, A.

Fellgett, P. B.

Foulger, S.

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics (Roberts & Company, 2007).

Guo, N.

Hang, Q.

Hirschfeld, T.

Kohlgraf-Owens, T. W.

Liew, S. F.

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7, 1–6 (2013).

Popoff, S. M.

Redding, B.

Sarma, R.

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7, 1–6 (2013).

Skorobogatiy, M.

Sullivan, M.

Syed, I.

Ung, B.

Wang, Z.

Xu, Z.

Appl. Opt. (1)

Appl. Spectrosc. (1)

J. Opt. Soc. Am. (1)

Nat. Photonics (1)

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7, 1–6 (2013).

Opt. Express (2)

Opt. Lett. (2)

Other (2)

P. B. Fellgett, “The multiplex advantage,” Ph.D. Thesis (University of Cambridge, 1951).

J. W. Goodman, Speckle Phenomena in Optics (Roberts & Company, 2007).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of photoelectron distributions over the detector pixels for a narrowband signal in the limited signal regime (a), (b) and limited well-depth regime (c), (d). (a), (c) are for a grating-based spectrometer and (b), (d) for a speckle-based spectrometer. In the limited signal regime (a), (b), the total number of photoelectrons is fixed. The grating-based spectrometer maps all the photons at a given wavelength to a single detector, whereas the speckle-based spectrometer spreads them over all the detectors. In the limited well-depth regime (c), (d), the maximum number of photoelectrons in a single pixel reaches the well depth of the detector. By spreading light in a single spectral channel over all spatial channels, the speckle-based spectrometer allows many more photoelectrons to be created and detected without saturating any pixels.

Fig. 2.
Fig. 2.

Reconstructed spectra for a narrowband probe in the limited signal regime using a grating-based spectrometer (a) or a speckle-based spectrometer (b) at three different signal levels (the total number of photoelectrons is marked next to each curve). The ideal probe spectra are plotted by the red-dotted lines and the measured spectra in the presence of noise by the blue solid lines. (c) Spectral reconstruction error, μ, as a function of signal level integrated over all wavelengths for the two types of spectrometers. The grating-based spectrometer is able to accurately measure the spectrum for signals about two orders of magnitude weaker than the speckle-based spectrometer in the limited signal regime.

Fig. 3.
Fig. 3.

Reconstructed spectra for a narrowband probe in the limited well-depth regime using a grating-based spectrometer (a) or speckle-based spectrometer (b) at three different detector well depths (indicated next to the curve). The ideal probe spectra are plotted by the red-dotted lines and the measured spectra in the presence of noise by the blue solid lines. (c) Reconstruction error, μ, as a function of the detector well depth for the two types of spectrometers. The speckle-based spectrometer provides slightly more accurate measurements than the grating-based spectrometer for narrowband probes in the limited well-depth regime.

Fig. 4.
Fig. 4.

Reconstructed spectra for probes with varying bandwidth (indicated by the FWHM, Δλ) in the limited signal regime using a grating-based spectrometer (a) or a speckle-based spectrometer (b). The ideal probe spectra are plotted by the red-dotted lines and the measured spectra in the presence of noise by the blue solid lines. (c) Comparison of the reconstruction error, μ, as a function of the signal bandwidth for the two types of spectrometers. The total number of photoelectrons over all spectral channels is set to 107. The grating-based spectrometer displays better accuracy in the limited signal regime, especially for broadband signals.

Fig. 5.
Fig. 5.

Reconstructed spectra for probes with varying bandwidth (indicated by the FWHM, Δλ) in the limited well-depth regime using a grating-based spectrometer (a) or transmission matrix based spectrometer (b). The ideal probe spectra are plotted by the red-dotted line and the measured spectra in the presence of noise by the blue solid line. (c) Comparison of the reconstruction error, μ, as a function of signal bandwidth for the two types of spectrometers. The detector well depth is set to 106 photoelectrons. For the narrowband spectra, the speckle-based spectrometer has similar accuracy to the grating-based spectrometer; however, the accuracy of the speckle-based spectrometer degrades with bandwidth while the grating-based spectrometer is relatively unaffected in the limited well-depth regime.

Fig. 6.
Fig. 6.

(a)–(d) Experimental speckle patterns produced by a multimode fiber at λ=1500nm at four levels of signal power in the limited signal regime. The total number of photoelectrons in each pattern is written on the top. (e) Spectra reconstructed from speckle patterns in (a), (b), (d). Even with only 7×106 photoelectrons, corresponding to the barely visible speckle pattern in (d), the peak wavelength of the probe signal is accurately identified. (f) Experimentally measured and numerically simulated spectral reconstruction error μ as a function of the total signal level (integrated over all detectors).

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