Spatial-frequency domain imaging coupled with frequency optimization for estimating optical properties of two-layered food and agricultural products
Introduction
There is continued interest in measuring optical absorption (μa) and reduced scattering (μs′) coefficients of food and agricultural products (e.g., milk, apple, mango and kiwifruit) as a means for enhancing nondestructive food quality and safety assessment (Hu et al., 2016, Van Beers et al., 2017, Liu et al., 2019, Zhang et al., 2019, Lu et al., 2020). Numerous optical techniques, such as spatially resolved (SR), time-resolved (TR), frequency domain (FD), and integrating sphere (IS) measurements, have been researched for optical property estimation over the past two decades (Hu et al., 2015). In most reported studies, samples were treated as homogeneous media so as to simplify the inverse parameter estimation algorithm. However, many food and agricultural products are composed of distinct layers with different optical properties, and the simplification can result in large, unacceptable errors in estimation as well as the loss of critical physicochemical information for individual layers. In the biomedical field, much research has been reported on estimating optical properties of two- and multi-layered turbid tissue using SR, TR, and FD techniques (Kienle et al., 1998, Liemert and Kienle, 2012, Wang et al., 2018), but the estimation errors are still too large and unacceptable due to much more complex parameter estimation algorithms.
As an emerging optical measuring technique, spatial-frequency domain imaging (SFDI) is capable of non-contact and wide-field mapping of μa and μs′. The technique has been applied for detecting apple internal browning by estimating the optical properties (Hu et al., 2016). Unlike conventional imaging techniques that rely on uniform illumination, SFDI is based on structured illumination for optical imaging of target samples. The μa and μs′ can be determined by fitting the demodulated reflectance on a pixel-by-pixel basis from the captured images using an analytical solution of diffusion model (Cuccia et al., 2009). Several studies have been reported for estimating μa and μs′ of layered tissues using the SFDI technique. Weber et al. (2009) employed SFDI for measuring μa and μs′ of two-layered custom-constructed optical phantoms and in vivo volar forearms at 650 nm, and they reported that the approach could provide noncontact mapping and quantification of layered tissue optical properties. Coupled with other techniques, such as artificial neural networks, SFDI was successfully used to decouple the effect of melanin absorption in the epidermis from blood absorption in the dermis, and it was able to independently measure optical thickness of the epidermis and the μa and μs′ of the dermis (Yudovsky and Durkin, 2011, Yudovsky et al., 2012). In these research, the optical properties (μa1, μs1′, μa2 and μs2′) of two-layered tissue were estimated simultaneously and large errors in estimating optical parameter(s) of the second layer were reported. For the convenience of discussion, hereinafter we refer to this estimation method as ‘all-at-once method’. In a previous study (Hu et al., 2019a, Hu et al., 2019b), we proposed a stepwise method, with which the μa and μs′ of one (often the top) layer is first estimated, followed by estimating μa and μs′ of the other layer. This method significantly improved the parameter estimation efficiency and accuracy, compared with the all-at-once method. In all previous studies for both methods, spatial frequency region (including frequency interval and start and end frequencies) was fixed for parameter estimations. However, inappropriate selection of frequency region could increase estimation errors because no a priori knowledge is available about the sample. Our study showed that frequency optimization in the SFDI technique resulted in overall improved accuracies in estimating μa and μs′ for one-layered, homogeneous turbid tissue (Hu et al., 2018). It is well understood that by adjusting spatial frequency (i.e., the number of fringes per unit path) of the illumination, SFDI allows depth-varying characterization of tissue optical properties; higher frequency results in shallower light interrogation and is thus more appropriate for estimating μa and μs′ of the top layer, while the illumination with lower frequency penetrates deeper into the tissues and undergoes more interaction with the bottom or second layer. Hence, it is feasible to improve optical property estimations for each layer of two-layered food and agricultural products, by using the stepwise method with different optimal frequencies for each layer.
This research was therefore aimed at optimizing the spatial frequency region (i.e., start and end frequencies) for improved estimation of the optical properties for two-layered food and agricultural products from spatial-frequency domain reflectance. The specific objectives were to: 1) determine optimal start and end frequencies for the inverse parameter estimation algorithm of the all-at-once method and stepwise method; 2) validate the optimized frequency region using Monte Carlo simulations and experiments with solid optical phantoms and liquid milk samples of known optical properties; and 3) measure the optical properties of skin and flesh of apple samples by using the stepwise method coupled with the optimized frequency region.
Section snippets
Principle of SFDI for estimating optical properties
Diffusion approximation equation (DAE) is a simplified form to the radiative transfer equation, based on the assumption that light distribution is almost isotropic in a scattering dominated medium (i.e., μs′ ≫ μa), which applies to most food and agricultural products in the visible and short-wave near-infrared spectral range of 500-1,300 nm. Consider a homogeneous one-layered medium of semi-infinite geometry normally illuminated at its surface by a steady-state, planar sinusoidal light pattern,
Optimization of the spatial frequency region
Fig. 6 shows the absolute error contour maps for estimating μa1 and μs1′ (top panel), and μa2 and μs2′ (bottom panel) by the stepwise method when using different start and end frequencies. Generally, the error values and variation range of μa were much larger than those of μs′, which was expected because μs′ is much greater in value than μa. For the first layer [Fig. 6(a1) and (a2)], it was observed that smaller start and end frequencies had a more pronounced effect on estimating μa1 compared
Discussion
Above results indicated that pattern of the μa and μs′ in 650–830 nm measured by the improved stepwise method could match that of the reference method (single IS technique), but the error values for μa2 were relatively large, especially at the wavelengths of 650 nm, 670 nm, and 690 nm. Besides the theoretical difficulty in estimating μa2, it was also due to the low SNR at these three wavelengths caused by high chlorophyll absorption. The high absorption may also reduce the accuracy of diffusion
Conclusion
A stepwise method was proposed for implementing SFDI technique to improve the estimation of μa and μs′ for two-layered food and agricultural products. Optimization of the spatial frequency region (i.e., start and end frequencies) was carried out for parameter estimations of each layer. Estimation accuracies for the proposed stepwise method coupled with the optimized frequency region were validated through Monte Carlo simulations and experiments for two-layered solid phantoms and liquid milk
Author contributions section
Dong Hu and Renfu Lu designed and conducted the experiments. Renfu Lu and Yibin Ying came up with the idea, provided overall supervision and guidance on the experimental aspects. Dong Hu conducted the simulations, analyzed the data and wrote the manuscript. All authors discussed the results and commented on the manuscript.
Disclaimer
Mention of commercial products is solely for providing factual information, and it does not imply the endorsement of the products by USDA over those not mentioned.
Declaration of competing interest
None.
Acknowledgements
The research reported in the paper was carried out when the first author was a visiting Ph.D. student with the USDA/ARS research unit at Michigan State University, East Lansing, Michigan. This work is supported by the Open Project of Key Laboratory of Ministry of Agriculture [2016NYZD18003].
References (35)
- et al.
Relationship of the optical absorption and scattering properties with mechanical and structural properties of apple tissue
Postharvest Biol. Technol.
(2013) - et al.
Assessing firmness and SSC of pears based on absorption and scattering properties using an automatic integrating sphere system from 400 to 1150 nm
Postharvest Biol. Technol.
(2016) - et al.
A two-step parameter optimization algorithm for improving estimation of optical properties using spatial frequency domain imaging
J. Quant. Spectrosc. Radiat. Transf.
(2018) - et al.
Nondestructive detection of underlying moldy lesions of apple using frequency domain diffuse optical tomography
Postharvest Biol. Technol.
(2019) - et al.
Quality assessment of tomato fruit by optical absorption and scattering properties
Postharvest Biol. Technol.
(2018) - et al.
Analytical approach for solving the radiative transfer equation in two-dimensional layered media
J. Quant. Spectrosc. Radiat. Transf.
(2012) - et al.
Effect of a plant growth regulator on optical properties of kiwifruit during growth in wavelength range of 950-1650 nm
Postharvest Biol. Technol.
(2019) - et al.
Measurement of optical properties of fruits and vegetables: a review
Postharvest Biol. Technol.
(2020) - et al.
Measurement of the optical properties of fruits and vegetables using spatially resolved hyperspectral diffuse reflectance imaging technique
Postharvest Biol. Technol.
(2008) - et al.
Relationship between tissue firmness and optical properties of ‘Royal Gala’ apples from 400 to 1050nm
Postharvest Biol. Technol.
(2014)