# Mexican Bee Honey Identification Using Sugar Crystals' Image Histograms
## 3 Results and Discussion  
### Validation and Repeatability  
In order to validate and test the repeatability of the proposed methodology in the honey's sugar crystals, an analysis using different excitation wavelengths was performed. Here, the response for each kind of honey at every excitation wavelength is analyzed, and this comparison will help to determine if they are repeatable. Additionally, for every wavelength, it will be possible to validate whether the methodology identifies each kind of honey independently of the rest. The selected honey samples for these tasks include orange (OG), mangrove (MG), and mesquite (MQ) honey. These three honey samples were selected as they have particular crystal morphological differences, representing an annual production of hundreds of tons in Mexico. The method began by taking a sample of each kind of honey to perform a process to match their crystallization times. So, each sample was poured into a Petri dish (Kimax, borosilicate glass, 60 mm \(\times\) 155 mm), which was warmed inside of a bowl with water maintained below 50 \({}^{\circ}\)C for 3 min. This time was enough to eliminate most of the crystals and to produce a liquid honey. Each honey set was stored at room temperature inside of a dark cabinet for two weeks for the first recording (S1). The previous process aimed to give each kind of honey the same time to crystallize regardless of its floral origin. For this purpose, each set of the three samples was recordedat different times. For example, samples from set 1, MG-S1, MQ-S1, and OG-S1, have the same crystallization time of two weeks, while MG-S2, MQ-S2, and OG-S2 have the same crystallization time of three weeks. Each sample for a set was then placed in a multiphotonic microscope, and an SHG image was recorded at one excitation wavelength at a time. In order to validate the proposed analysis, 20 different excitation wavelengths along the microscope's range (840 up to 1060 nm) were used, resulting in 20 images for each sample. The latter helps to observe the SH grouping response of the honey's crystals according to the excitation wavelength once processed. After that, an SHG imaging database of honey images was obtained, where the same illumination conditions were used in all of the samples. If the images shown in Figure 2 are observed, a morphological analysis using digital image processing algorithms could be an option to retrieve the differences among their crystals. However, besides the time required for this task, the crystals are not aligned to a perpendicular plane in the observation direction. They are all stacked at different depths and overlap, making it difficult to identify and measure them independently, especially in the case of the mesquite honey. For this reason, a simpler and more direct method is proposed as proof-of-principle for these SHG images [31; 32]. The used histograms were directly generated with the microscope suite, which records this information in a file as an array. Nevertheless, an independent algorithm in Matlab was used to corroborate the counts. Considering that the gray-level images obtained with the microscope were retrieved with a depth of 8 bits, each histogram will have 256 available gray levels. Figure 3a-c shows representative examples of the gray-level histogram profiles for the honey samples. They are retrieved when the sample is irradiated with an excitation wavelength (\(\lambda_{\text{E}}\)) of 840, 940, and 1040 nm to have an SHG emission (\(\lambda_{\text{SH}}\)) at 420, 470, and 520 nm, respectively (as indicated in Figure 1). The histograms in Figure 3 represent a highly contrasted image closer to a binary response. Here, the black and bright gray levels keep most of the counts, while the intermediate gray levels are near zero (for clarity, the \(y\)-axis is shown in logarithmic form). In fact, with the histograms, it is impossible to observe a distinctive tendency for each kind of honey or to differentiate among them.