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Nonnegative matrix factorization numerical method has been used to improve the spectral resolution of integrated photonic cavity based spectroscopy. Based on the experimental results for integrated photonic cavity device on Optics Letters 32, 632 (2007), the theoretical results show that the spectral resolution can be improved more than 3 times from 5.5 nm to 1.8 nm. It is a promising way to release the difficulty of fabricating high-resolution devices.

Miniature spectrometers are important for a wide variety of applications such as biomedical, chemical, remote sensing, and environmental engineering [

An interesting problem is to improve the spectral resolution by numerical model on this concept of high-resolution miniature spectrometer. Since the filtering properties of the integrated photonic cavity may not be ideal, the transmission spectrum of each photonic cavity channel may have large ripples on pass- and stopbands and poor stopband attenuation [

In order to improve the spectral resolution of the integrated photonic cavity, one method is to fabricate more narrowband integrated photonic cavity devices, but that is an extremely difficult and expensive work. Digital signal processing is another low-cost way to improve the spectral resolution. Several approaches have recently been exploited, such as sparse nature of signals [

As a new method to reconstruction of image, the nonnegative matrix factorization (NMF) has been developed, which uses nonnegativity constraints and results in a parts-based representation [

Our goal is to investigate the effect in terms of resolution improvement by using NMF numerical method. Using the concept of high-resolution miniature spectrometer [

For the whole wave band covered by integrated photonic cavity, from

For convenience, the above matrix form can be expressed as a concise form:

From the point of digital signal processing,

In this work, we chose

The

The rank

Obtaining the

NMF numerical method does not allow negative entries in the matrix factors

The experimental spectral results of 128 integrated photonic cavities device reported by Wang et al. [

Experimental spectra of the 128-channel integrated filter array cited from [

To demonstrate the function of the NMF numerical method, we reconstruct the target spectrum on Optics Letters 32, 632 (2007) [

Comparison of resolution ability for integrated photonic cavity spectrometer itself [

To evaluate the suitability of the NMF numerical method, several typical targets spectra with different structures were reconstructed by the NMF numerical method, including a typical two-peak structure spectrum, a typical fluorescence spectrum with sharp ascending and slowly descending branch, and a typical infrared transmission spectroscopy with characteristic absorption peaks. In Figures

The reconstruction of a typical two-peak structure with interval of 8 nm.

The reconstruction of a typical fluorescence spectrum with sharp edges and asymmetric peak structure.

The reconstruction of a typical infrared transmission spectroscopy with characteristic absorption peaks.

Comparison of resolution ability for target spectrum and the reconstructed spectrum by NMF method. The peak interval of the target is 1.8 nm.

For a target spectrum with two-peak structure whose interval is 8 nm, both the integrated photonic cavity spectrometer itself and that accompanied with our method can distinguish two peaks as shown in Figure

For a typical fluorescence spectrum with sharp ascending and slowly descending branch [

Similarly, for a typical infrared transmission spectroscopy with characteristic absorption peaks, the filter channels covering the absorption peaks are limited, leading to serious information loss and distorted spectral structures. As shown in Figure

To evaluate the resolution limit of the 128 integrated photonic cavities device using NMF numerical method, a series of two-peak structure spectra with different interval were reconstructed, especially when the peak interval of target decreases to smaller than 5.5 nm, which is beyond the resolution limit of 128 integrated photonic cavities device reported in [

In this work, NMF method has been used to improve the spectral resolution of integrated photonic cavity based spectroscopy. The numerical results show that it will agree with the original target better with the aid of NMF method. The spectral resolution can be improved from 5.5 nm to 1.8 nm, 3 times better than without the aid of NMF method.

The authors declare that they have no conflict of interests regarding the publication of this paper.

This work was supported by the Shanghai Science and Technology Foundations (11nm0502100, 12nm0502900, and 11nm0503600) and partially supported by the National Nature Science Foundation of China (no. 61106092 and no. 11374213).