Dataset for Snapshot fiber spectral imaging using speckle correlations and compressive sensing
DOI:10.5258/SOTON/D0698

Readme Author: Otto Muskens, University of Southampton

Supports the paper
 
French, R., Gigan, S., & Muskens, O. L. (2018). Snapshot fiber spectral imaging using speckle correlations and compressive sensing. Optics Express, 26(24), 32302-32316. DOI: 10.1364/OE.26.032302

Figure 1

Spectral correlation functions of a 30 cm- length of multicore multimode fiber (MCMMF), each fiber with a core diamter of 50 microns. 

Contents of ASCII data:

1(d) Fig1d_narrow.txt. The fibers using a tunable continuous wave diode laser. Wavelength-dependent speckle patterns were measured, in increments on the order of 10^-1 nm, and cross-correlated
 with a speckle pattern corresponsing to wavelength 778.2 nm. The resulting normalised correlation coefficients were plotted against the recorded change in wavelength. 
 The spectral correlation width was found to be 1.4 nm.

1(d) Fig1d_broad.txt. The fibers using the calibration laser with bandwidth approximately equal to 1 nm. Wavelength-dependent speckle patterns were measured, in increments of approximately 0.4 nm,
and cross-correlated with a speckle pattern corresponsing to wavelength 692 nm. The resulting normalised correlation coefficients were plotted against the change in 
wavelength.  The spectral correlation width was found to be 2.1 nm.




Angle dependence of multicore multimode fibers (MCMMFs). Angular correlation functions were measured by cross-correlating one speckle pattern corresponding to a particular incident angle 
with consecutive speckle patterns after altering the incident angle by a small increment. This was carried out for a MCMMF of 30 cm. The corresponding angular correlation widths were 
found by determining the full width half maximum of the correlation functions.


Contents of ASCII data:


1(e)

Images:

Supp3im_0.txt. Image of speckle patterns produced by light entering the MCMMF with a 0 degree incident angle.
Supp3im_2.txt. Image of speckle patterns produced by light entering the MCMMF with a 2 degree incident angle.
Supp3im_4.txt. Image of speckle patterns produced by light entering the MCMMF with a 4 degree incident angle.


Correlation widths:

Supp3x_0.txt. x values corresponding to the change in angle (degrees).
Supp3y_0.txt. y values corresponding to the correlation coefficients produced by cross-correlating a speckle produced by 0 degree incident light and 
consecutive speckle patterns when the incident angle is displaced by a small amount.
Supp3y_0_l.txt. Lower limits defined by one standard deviation, calculated across all fiber cores.
Supp3y_0_u.txt. Upper limits defined by one standard deviation, calculated across all fiber cores.

Supp3x_2.txt. x values corresponding to the change in angle (degrees).
Supp3y_2.txt. y values corresponding to the correlation coefficients produced by cross-correlating a speckle produced by 2 degree incident light and 
consecutive speckle patterns when the incident angle is displaced by a small amount.
Supp3y_2_l.txt. Lower limits defined by one standard deviation, calculated across all fiber cores.
Supp3y_2_u.txt. Upper limits defined by one standard deviation, calculated across all fiber cores.

Supp3x_4.txt. x values corresponding to the change in angle (degrees).
Supp3y_4.txt. y values corresponding to the correlation coefficients produced by cross-correlating a speckle produced by 4 degree incident light and 
consecutive speckle patterns when the incident angle is displaced by a small amount.
Supp3y_4_l.txt. Lower limits defined by one standard deviation, calculated across all fiber cores.
Supp3y_4_u.txt. Upper limits defined by one standard deviation, calculated across all fiber cores.


Figure 2

Schematic of the spectral imaging system demonstrating the transmission matrix design and development.

Contents of ASCII files:

(1) Fig2image.txt. Cross-section of the output of a 30 cm-long multicore multimode fiber (MCMMF), each with core diameter of 50 microns, 
imaged on a 12-bit 5 MPixel CMOS array of 2.2 micron by 2.2 micron pixel size, using a wavlength of 674 nm.

(2) Fig2tmat1.txt, Fig2tmat2.txt, Fig2tmat3.txt, Fig2tmat4.txt. Slices of the transmission matrix for 43 spectral channels separated by 0.37 nm, with each slice corresponding to a different fiber core. 
The 3D transmission matrix was built by extracting an area of interest (441 pixels) from the wavelength-dependent speckle patterns produced by each fiber core. The pixel areas were reshaped into column 
vectors and stored in the transmission matrix corresponding to the correct wavelength and core coordinate.


Figure 3 (a)

Reconstruction ability when sampling above and below the Nyquist-Shannon limit for a sparse spectral signal (N_lambda = 1) and a more complex spectrum (N_lambda = 10).

A transmission matrix was calibrated using Y pixels and X spectral channels, and used to reconstruct sparse and complex spectral information. The resulting reconstruction was cross-correlated with a "perfect" reconstruction.
This was repeated for many values of Y.



Contents of ASCII files:

(1) Fig3a.txt. x values corresponding to Y/X for subsequent correlation files.

(2) Fig3a_1.txt. y values corresponding to the correlation between a "perfect" reconstruction and the reconstruction using a particular Y/X for N_lambda = 1.

(3) Fig3a_10.txt. y values corresponding to the correlation between a "perfect" reconstruction and the reconstruction using a particular Y/X for N_lambda = 10.



Figure 3(b)

Reconstruction ability of the spectral imaging system with increased spectral complexity, i.e. as the number of wavelengths increases. 
Correlation coefficients are determined between a "perfect" spectral reconstruction and the experimental spectral reconstruction after 
the number of wavelengths in each spectrum increases by one. The standard deviation is calculated over all fiber cores.

Contents of ASCII files:

(1) Fig3b_xvalues.txt. x values corresponding to the number of wavelengths contained within the spectrum to be reconstructed, 
and the ratio of the number of wavelengths to the number of spectral channels.
(2) Fig3b_b.txt. The correlation coefficients between "perfect" and experimental reconstruction when transmission matrix is calibrated using Y camera pixels and X spectral channels, Y/X=0.84.
(3) Fig3b_bu.txt. The upper limits (one standard deviation) when Y/X=0.84.
(4) Fig3b_bl.txt. The lower limits (one standard deviation) when Y/X=0.84.
(5) Fig3b_r.txt. The correlation coefficients between "perfect" and experimental reconstruction when transmission matrix is calibrated using Y camera pixels and X spectral channels, Y/X=1.1.
(6) Fig3b_ru.txt. The upper limits (one standard deviation) when Y/X=1.1.
(7) Fig3b_rl.txt. The lower limits (one standard deviation) when Y/X=1.1.
(8) Fig3b_g.txt. The correlation coefficients between "perfect" and experimental reconstruction when transmission matrix is calibrated using Y camera pixels and X spectral channels, Y/X=10.3.
(9) Fig3b_gu.txt. The upper limits (one standard deviation) when Y/X=10.3.
(10) Fig3b_gl.txt. The lower limits (one standard deviation) when Y/X=10.3.


Figure 3(c), (d), (e)


Contents of ASCII files:

(c) Fig3c.txt. An image of a speckle pattern produced by 1 fiber core, corresponding to coordinate (918, 1249) and wavelength 674 nm.


(d)(1) Fig3M_im. Camera image showing the letter "M" with wavelength 674 nm after propagating thorugh a 30 cm-length of multicore multimode fiber (MCMMF) with 50 micron cores. 

(d)(2) Fig3M_coord.txt, Fig3M_coord2.txt. x and y coordinates determined by the clustering algorithm DBSCAN, define spatial coordinates used during transmission matrix calibration.


(e) Reconstructions of the letter M from Figure 3(d) using 4 different values of Y/X (number of pixels selected from each fiber core for transmission 
matrix calibration/number of spectral channels):

(1) Fig3e1.txt. Y/X = 0.14
(2) Fig3e2.txt. Y/X = 0.32
(3) Fig3e3.txt. Y/X = 0.90
(4) Fig3e4.txt. Y/X = 2.03


Figure 3(f)

Reconstruction ability in environments of varying degrees of noise.

A transmission matrix was calibrated by selecting Y pixels from each fiber core in a multicore multimode fiber of length 30 cm and core diamter of 50 microns, for X spectral channels.
The transmission matrix was used to reconstruct spectral information, and was also used as the "output". Articial i.i.d. noise was added to the output in increasing amounts (0% - 50% in steps of 5%).
The reconstructions were cross-correlated with a "perfect" reconstruction and the resulting normalised correlation coefficients were observed. The standard deviation was calculated over 
the correlation coefficients for the reconstructions of every fiber.

Contents of ASCII files:

(1) Fig3f_1.txt. Correlation coefficients for Y/X= 10.3.
(2) Fig3f_1l.txt. Correlation coefficients upper limits (one standard deviation) for Y/X= 10.3.
(3) Fig3f_1u.txt. Correlation coefficients lower limits (one standard deviation) for Y/X= 10.3.

(4) Fig3f_2.txt. Correlation coefficients for Y/X= 1.1.
(5) Fig3f_2l.txt. Correlation coefficients upper limits (one standard deviation) for Y/X= 1.1.
(6) Fig3f_2u.txt. Correlation coefficients lower limits (one standard deviation) for Y/X= 1.1.

(7) Fig3f_3.txt. Correlation coefficients for Y/X= 0.84.
(8) Fig3f_3l.txt. Correlation coefficients upper limits (one standard deviation) for Y/X= 0.84.
(9) Fig3f_3u.txt. Correlation coefficients lower limits (one standard deviation) for Y/X= 0.84.

Figure 4

Hyperspectral snapshot reconstruction of 16 letters each of a different wavelength. The transmission matrix was built using a pixel to spectral channel ratio of Y/X = 4.
The transmission matrix was applied to every fiber core and the corresponding spectra were reconstructed at each spatial channel.

Contents of ASCII files:

(a) Fig4a_all.txt. x and y values of a reconstructed spectrum between 696 nm and 654 nm, for a fiber core position corresponding to centre coordinates (1139, 1023) in (b).
The known 9 wavelengths (measured using an Ocean Optics spectrometer) are also given.

(b) Fig4im.txt. Composite camera image made up of 16 letters, with each letter measured using a different wavelength (see (d)).

(c) Fig4c_all. x and y values of a reconstructed spectrum between 696 nm and 654 nm, for pixel corresponding to (1283, 1268) in (b).
The known 3 wavelengths (measured using an Ocean Optics spectrometer) are also given.

(d) Reconstructed spatial information using a transmission matrix. 
Letters: 
(1) Fig4A.txt. Corresponding to a wavelength of 691.6 nm.
(2) Fig4C.txt. Corresponding to a wavelength of 689.7 nm.
(3) Fig4E.txt. Corresponding to a wavelength of 687.7 nm.
(4) Fig4F.txt. Corresponding to a wavelength of 685.8 nm.
(5) Fig4H.txt. Corresponding to a wavelength of 684 nm.
(6) Fig4I.txt. Corresponding to a wavelength of 681.8 nm.
(7) Fig4J.txt. Corresponding to a wavelength of 680.1 nm.
(8) Fig4K.txt. Corresponding to a wavelength of 677.9 nm.
(9) Fig4L.txt. Corresponding to a wavelength of 675.9 nm.
(10) Fig4M.txt. Corresponding to a wavelength of 674.2 nm.
(11) Fig4N.txt. Corresponding to a wavelength of 672 nm.
(12) Fig4P.txt. Corresponding to a wavelength of 670 nm.
(13) Fig4R.txt. Corresponding to a wavelength of 667.9 nm.
(14) Fig4S.txt. Corresponding to a wavelength of 665.9 nm.
(15) Fig4T.txt. Corresponding to a wavelength of 663.8 nm.
(16) Fig4U.txt. Corresponding to a wavelength of 661.9 nm.

Figure S1

Spectral dependence of multicore multimode fibers (MCMMFs). Two spectral correlation functions were measured by cross-correlating one speckle pattern corresponding to a particular wavelength 
with consecutive speckle patterns after changing the wavelength by a small increment. This was carried out for a MCMMF of 2.5 cm and 15 cm. The corresponding spectral correlation widths were 
found by determining the full width half maximum of the correlation functions. The spectral correlation widths were plotted against the respective inverse of the length of the MCMMF.


Contents of ASCII files:

(S1a) 

Supp1ax.txt. x values corresponding to the change in wavelength (nm).
Supp1ay.txt. y values corresponding to the correlation between the speckle pattern produced by 692 nm-light travelling through a 2.5 cm MCMMF and consecutive speckle patterns.
Supp1ay_l.txt. Lower limits of error bars (one standard deviation) calculated over all fiber cores.
Supp1ay_u.txt. Upper limits of error bars (one standard deviation) calculated over all fiber cores.


(S1b)

Supp1bx.txt. x values corresponding to the change in wavelength (nm).
Supp1by.txt. y values corresponding to the correlation between the speckle pattern produced by 692 nm-light travelling through a 15 cm MCMMF and consecutive speckle patterns.
Supp1by_l.txt. Lower limits of error bars (one standard deviation) calculated over all fiber cores.
Supp1by_u.txt. Upper limits of error bars (one standard deviation) calculated over all fiber cores.


(S1c)

Supp1cx_cor.txt. x values corresponding to the inverse of the length of the MCMMF (300 mm, 150 mm, 25 mm).
Supp1cy_cor.txt. y values corresponding to the spectral correlation width of the MCMMF.
Supplcy_fit.txt. Fit plotted to data using MATLAB function polyfit.
Supplcy_st_u.txt. Upper limits of error bars (one standard deviation) calculated by interpolating the corresponding spectral correlation functions.
Supplcy_st_l.txt. Lower limits of error bars (one standard deviation) calculated by interpolating the corresponding spectral correlation functions.

Figure S2

Reconstruction of spatial information across 4 different spectral bands (wavelength = 678.5~nm, 674.6~nm, 674.2~nm, 673.8~nm) for 2 different sampling rates Y/X = 4 and Y/X=0.32, respectively.
A letter-shaped aperture was illuminated with light corresponding to a central wavelength of 674.1~nm. A calibrated STM consisting of 111 spectral channels was used to reconstruct the input 
information.

Contents of ASCII files:

(S2a) 


M_50.txt. Reconstruction of input signal with a sampling rate of Y/X=4 for spectral channel at 678.5~nm.
M_60.txt. Reconstruction of input signal with a sampling rate of Y/X=4 for spectral channel at 674.6~nm.
M_61.txt. Reconstruction of input signal with a sampling rate of Y/X=4 for spectral channel at 674.2~nm.
M_62.txt. Reconstruction of input signal with a sampling rate of Y/X=4 for spectral channel at 673.8~nm.
M_63.txt. Reconstruction of input signal with a sampling rate of Y/X=4 for spectral channel at 673.4~nm.
M_64.txt. Reconstruction of input signal with a sampling rate of Y/X=4 for spectral channel at 673.0~nm.

(S2b)

M_032_50.txt. Reconstruction of input signal with a sampling rate of Y/X=0.32 for spectral channel at 678.5~nm.
M_032_60.txt. Reconstruction of input signal with a sampling rate of Y/X=0.32 for spectral channel at 674.6~nm.
M_032_61.txt. Reconstruction of input signal with a sampling rate of Y/X=0.32 for spectral channel at 674.2~nm.
M_032_62.txt. Reconstruction of input signal with a sampling rate of Y/X=0.32 for spectral channel at 673.8~nm.
M_032_63.txt. Reconstruction of input signal with a sampling rate of Y/X=0.32 for spectral channel at 673.4~nm.
M_032_64.txt. Reconstruction of input signal with a sampling rate of Y/X=0.32 for spectral channel at 673.0~nm.

Figure S3

Angle dependence of multicore multimode fibers (MCMMFs). Angular correlation functions were measured by cross-correlating one speckle pattern corresponding to a particular incident angle 
with consecutive speckle patterns after altering the incident angle by a small increment (Figure 1). This was carried out for a MCMMF of 30 cm. The corresponding angular correlation widths were 
found by determining the full width half maximum of the correlation functions. The angular correlation widths were plotted against the respective initial incident angle.


Contents of ASCII files:


Supp3x_cor.txt. x values corresponding to the incident angle of light propagating through the MCMMF.
Supp3y_cor.txt. y values corresponding to the respective angular correlation widths for a particular incident angle of light.
Supp3y_cor_u.txt. Upper limits of error bars (one standard deviation) calculated by interpolating the corresponding spectral correlation functions.
Supp3y_cor_l.txt. Lower limits of error bars (one standard deviation) calculated by interpolating the corresponding spectral correlation functions.

Licence: Attribution 4.0 International (CC BY 4.0) https://creativecommons.org/licenses/by/4.0/

December, 2018