Terahertz time domain spectroscopy technique used for evaluation of thickness and optical cum dielectric properties of table and fertile eggshells

Abstract

The paper reports the use of THz time domain spectroscopy for the measurements of thickness, refractive index and dielectric constants of chicken egg shells. Twelve numbers of table and fertile egg samples were selected. The experiment was performed in the reflection geometry using a fiber-coupled terahertz source between 0 and 4.0 THz range. The reflected time domain signal from the inner eggshell-membrane boundary and the outer eggshell interface was used, to determine shell thickness. The results were verified with Field Emission Scanning Electron-Microscopy (FESEM). In the next step, the obtained Time/frequency domain spectra data were used to ascertain the R.I., absorption coefficients, and real and imaginary parts of the dielectric constants for the first time. It was noticed that the values of R.I. of normal eggs at 0.8 THz were higher than 2.5 as compared to fertile eggs. Similarly, the absorption coefficient values for nonfertile eggs lie between 2 and 14 cm ⁻¹ compared to fertile eggs, which lie between 2 and 10 cm ⁻¹ range.The most important aspect of our study is related to measurements of real and imaginary parts of dielectric constants between 1.2 and 3.0 THz range the nonfertile eggs show a steep drop in values between 4 − 2.0 range while fertile eggs show an almost linear response of 4 0.0 in the given frequency range. The imaginary parts show nonfertile egg values between 7.0 and 3.75 while fertile eggs show a consistent result of the order of 5.0. It further opens a new channel to enhance the poultry industry. The results were verified using field emission scanning electron microscopy results. This non-destructive technique can play a very important role in the poultry industry in minimizing waste and maximizing efficiency.

Introduction

The eggshell is a protective barrier for the developing embryo from external contaminations and UV radiation. It facilitates gas exchange from the surface and acts as a source of minerals for the developing biological system in avian birds¹. Thin eggshells cause cracks, infection, and dehydration, leading to higher embryonic mortality. The quality of the eggshells is essential for better hatching and preventing egg breakage². The estimated economic losses from cracked and broken eggs constitute between 6% and 8% of the total eggs produced³. On one hand, the higher thickness provides higher mineral resources and protection while, on the other side, it makes the job of storage and transportation easier. Therefore, a non-destructive thickness measurement technique is highly desirable in meat and egg production. Also, eggshells are a barrier to many acoustic and optical spectroscopic research approaches, for instance, ovo sexing by optical spectroscopy. Determination of sex at an earlier stage is a prerequisite for solving unwanted male chick culling⁴. Because eggshells are a hindrance to embryo probes.

The measurement of eggshell thickness is a crucial exercise in quality control processes and investigating the effects of pollutants and environmental contamination on its thinning. Accurate data on eggshell thickness can quantify the hazardous effects of pesticides, chemical wastes, and pollutants on the egg quality of various types of species.

Different types of laboratory-based techniques have been employed to measure eggshell thickness, these are further divided into destructive and non-destructive categories. Eggshell thickness measurements are often done using destructive methods like drilling air holes with micrometer screws, impact fracture force, puncture force, or quasistatic compression⁵. The quality of the egg is influenced by the uniformity of eggshell thickness rather than the thickness itself⁶. Researchers measured eggshell thickness along longitudinal and latitudinal axes using a gauge, finding significant variations from blunt to sharp end. Non-destructive methods involve dipping eggs in salt solutions with different concentrations of salt, allowing for rapid testing⁷. However, these methods have the disadvantage of giving crude results. Ultrasound has also been shown to be successful in measuring eggshell thickness non-destructively⁸. Applying the photonic imaging modality of optical coherence tomography, intact egg thickness can be measured. The OCT can measure eggshell thickness and detect cracks up to 1.7 mm resolution. However, measuring thin and fragile eggshells with this method is a challenging task. Commercial ultrasonic sensors, such as the Egg Tester Precision Ultrasonic Egg Shell Thickness Gauge and non-ferrous material Thickness Gauge, are available for non-destructive measurements⁹. The Magna-Mike 8600 and Mini-Test 7200 FH Hall-effect thickness gauges (HETG) are used to measure the thickness of eggshells and membranes. These non-destructive devices measure the distance between a steel reference ball and a magnetic probe, providing precise and accurate digital measurements. HETG measurements are similar to Starrett thickness gauges but generally 0–9% thicker. As compared to pre-DDT-era eggshells, HETG measurements are about 12% thicker. The HETG is a useful device for accurate and repeatable measurements, especially for smaller, fragile eggs, without damaging the eggshells¹⁰. However, this process requires the careful handling of eggs. When electromagnetic waves are used for eggshell thickness probes, the brown-colored pigment of eggs shows high absorbance and scattering effects that make use of UV and visible electromagnetic waves unsuitable for non-destructive measurement.

Besides the thickness of the eggshells, extinction coefficient and dielectric properties are some other important parameters to evaluate the quality of egg, which diminishes during storage. The Haugh unit and yolk index are some useful indicators to ascertain the quality of the Egg. The dielectric constant and loss factor of egg albumen and yolk over the 10 to 1800 MHz frequency range during 5-week storage at 15 °C are reported. The reported results show that albumen had higher dielectric constants and loss factors than the yolk. The dielectric constants rose after 2 weeks in storage, remaining constant throughout the 5 weeks. Since the storage has less influence on the albumen or yolk loss factor. Therefore, no correlation is observed between dielectric properties and moisture content, ash content, Haugh unit, or yolk index¹¹.

Dielectric characteristics are essential for detecting chemical structures and distinguishing molecule combinations. These characteristics can help to determine the quality of mixed-material complexes. Some other studies discuss the use of dielectric spectroscopic methods for evaluating the agricultural items, exploring connections between dielectric qualities and other physical and chemical data. Agricultural materials and food have frost sensitivity, chilling and freezing tolerance, moisture content, seed germination, mechanical stress, pasteurization, and insect control in contaminated food¹² are shown in Table 1.

Table 1.

Comprises the Dielectric properties of egg’s liquid ingredients at different frequencies.

Sl.No.	Sample	Moisture			T (°C)	f(MHz)	dp*(mm)
1	Liquid egg white	85.0	81.3	646.4	60	27	52.4
2	Liquid egg white	85.0	98.3	866.5	80	27	45.0
3	Liquid egg white	85.0	51.5	25.3	60	915	15.9
4	Liquid egg white	85.0	50.5	33.3	80	915	12.2
5	Egg (white) albumen	87–89	67.2	22.3	20	2450	7.3
6	Egg (white) albumen	87–89	60.7	20.3	40	2450	7.6
7	Egg yolk	47.0	41.4	12.1	20	2450	10.5
8	Egg yolk	47.0	37.1	10.0	40	2450	12.0

Due to their high nutritional content, eggs can harbor and transmit harmful microorganisms, such as Salmonella enteritidis. According to FSIS-USDA (2006), heat pasteurization is often considered the most effective method for controlling these disease-causing microorganisms. A study was carried out to examine the impact of temperature and frequency on the dielectric characteristics of egg components. The results indicate that albumen exhibits greater dielectric values and faster rapid heating rates than yolk. Nevertheless, both egg components and egg yolks exhibit comparable heating rates. Microwave heating shows significant promise for the pasteurization of eggs while still in their shells. Furthermore, this paper presents models for determining heating rates¹³. Materials’ dielectric characteristics are important for assessing electromagnetic energy interactions, particularly in the food industry. These attributes depend on frequency, temperature, composition, and moisture. A review compared microwave or radio wave penetration depths across food classes based on their dielectric properties. Food type and frequency have an impact on temperature and composition. Finding the best dielectric heating approach requires more research. The dielectric characteristics of food items depend on moisture and conductivity¹⁴.

The dielectric properties of eggshell powder measured between 2.45 and 5.8 GHz, microwave frequency range under altering temperature and moisture content (15–75 °C and 0.5-8% (wet basis)) utilizing the cavity perturbation technique. The values of  and rise with temperature and moisture content at both frequencies. However,  shows a higher value at 2.45 GHz than 5.8 GHz, and shows the reverse tendency. According to research, microwave penetration depths are higher at 2.45 GHz than at 5.8 GHz and decrease with temperature and moisture content. Third-order regression equations with good correlation coefficients (R2 > 0.95) were generated using data from  and . Findings aid in modeling and developing microwave applicators for eggshell powder heat treatment¹⁵ Another study measured the dielectric constant, loss angle, and dissipation characteristics of eggshell membranes for several bird species at a frequency of 1 kHz. The dielectric constants of Hen, Layer, Duck, Turkey, and Quail were 6.016, 5.556, 6.809, 6.145, and 2.632, respectively. As the frequency reached 3 GHz, a drop in the value of dielectric constants along with loss in angle and dissipation factor were observed. Eggshell membranes provide both sustainability and affordability, making them highly suitable for manufacturing capacitors in the electrical and electronic industries¹⁶.

D.S. Citrin et al. have reported the THz-based measurement of multiple layer thickness and characterization of glass fiber-reinforced polymer (GFRP) laminates using the adaptive sparse deconvolution method, They have also extended this technique to multi-layer coated steel by terahertz time-of-flight tomography^17,18. Soufiene Krimi et al. have reported the highly accurate thickness measurements of multilayered automotive paints using terahertz time domain spectroscopy in reflection geometry. They have applied a generalized Rouard’s method to simulate the terahertz radiation behavior within arbitrary thin films¹⁹.

Nicolas S. Beermann et al. have measured the optical and delectric parameters of several common dielectric materials such as MgO, Al₂O₃, GaAs, and SiO₂ using the THz-TDS technique in transmission mode and obtained deep-sublevel precision of the order of λ/1000²⁰. D-H Han reported the thickness and adhesion status of paint sensors using pulsed terahertz (THz) waves. The technique in the reflection geometry node is advantageous in a detailed assessment of thin films or multilayer paints²¹. However, terahertz (THz) radiation offers the most promising solution due to its numerous advantages, including low power and deep penetration through the shell, which enables information to be transmitted through the different layers of the eggshell in reflection mode. It is also supported by the low water content and crystalline nature of eggshells. Khaliduzzama et al. used TH_Z-TDS for the thickness measurement of white infertile eggs. A linear regression-based prediction model was developed for the non-destructive measurement of eggshell thickness. It had an RER of 13.67, an RMSEP of 0.009, an RPD of 3.45, and an R2 of 0.93 and provides precision of less than 10 µm²².

Terahertz-based spectroscopy is applied for the non-destructive analysis of samples in various domains, including industrial quality control²³. Reflection, transmission, and attenuation processes are three phenomena that are crucial to take into account when THz waves propagate at each interface—the air-shell, shell-membrane, and membrane-albumen interfaces—of an intact egg.

In the present work, we have used Terahertz Time-domain Spectroscopy in reflection mode for evaluating the important optical properties such as thickness, refractive index, absorption coefficient, and dielectric constants (real and imaginary) of table and fertile chicken eggshells between 0.1 and 3.0 terahertz frequency range. We have adopted the Maximum Entropy Method (MEM) technique, which is another effective version of the S. Krimi approach where reflected THz signals from the eggshell surface and the interfacing of the shell and membrane were recorded on a time domain scale. Due to high pulse duration and repetition rate, the two signals can clearly be distinguished on a pico seconds time scale without any interference. Further, we have modified the reflection geometry-based model of Khaliduzzaman A. and extended it to ascertain the important real and imaginary parts of the dielectric constants of eggshells. The THz transmission and reflection were tested on broken and undamaged eggshells, respectively. The eggshell’s refractive index increased slightly with increasing THz frequency, ranging from 2.7 to 3.3. However, the extinction coefficient increased dramatically from 0.2 to 2.0 THz.The obtained data are repeated a minimum of five times with a 100 MHz repetition rate (the 1000 pulses per second carry the same information from the surface of the eggshells. We have also cross-checked our results reported values lie between 2.3 and 3.3 range^24–26. The eggshell’s dielectric constant increased significantly from 7.0 to 10.2²⁷. The frequency domain interference signal of a sub-millimeter THz wave provided information on the eggshell’s thickness and refractive index, leading to the successful development of a technique for estimating the thickness of quail eggshells with a coefficient of determination (R2) of 0.79. Khaliuzzama et al. came up with a non-destructive sampling method; the refractive index (n) of quail eggs was between 2.35 and 2.35²⁸.

Materials and methods

All samples were sourced from PVNR Veterinary University Hyderabad. Fertile eggs were obtained from housing units where female and male chickens were kept for mating. However, Table eggs were sourced from housing units with only female chickens. The carefully selected potential fertile eggs are incubated in the facility. All sourced samples are brown eggs. We have selected twelve egg samples for the present study. Out of which six numbers of fertile egg samples were incubated for a day, the remaining six infertile a week-old refrigerated table chicken eggs for the determination of their thickness and other important physical parameters such as R.I., absorption coefficients, and real and imaginary parts of dielectric constants. We have used two important physical techniques, such as (i) FESEM and (ii) Time Domain THz Spectroscopy to measure the different physical parameters of the Egg samples.

In the first part, a cross-section of the eggshells was ascertained by scanning with an electron microscope to verify the accuracy and precision. It also helped to measure the thickness of the eggshells. The membranes of the shell were removed mechanically, and the thickness of eggshells and shell membranes were measured separately. However, a cross-section examination was done by making the shell piece face up and aligned parallelly with the screen boundary. two fertile and two infertile eggs were taken for thickness measurement with FESEM (Model Ultra 55 Carl Zeiss).

In the second part of the experiment, Terahertz time-domain spectroscopy was performed to measure the thickness of intact eggs. A commercial tabletop THz time-domain system (model TeraFlash-Toptica Photonics, Germany) with a bandwidth of over 4.0 THz and a peak dynamic range exceeding 90 dB was used for the measurement. The system employed an optical fiber-coupled femtosecond laser featuring a voice coil-driven corner mirror with a position sensor and InGaAs/InAlAs photoconductive antennas for THz generation. The femtosecond fiber-coupled laser (Toptica FemtoFErb THz FDS) operated at a central wavelength of 1560 nm, with a pulse width of 60 fs, a repetition rate of 100 MHz, and an average output power of 80 mW. The incident THz radiation was used to irradiate the egg samples at an 8-degree angle in reflection geometry. The system is purged with dry air to eliminate the effect of atmosphere humidity. The reflected time domain signal from the eggshell was then converted into a frequency domain signal using a fast Fourier transform (FFT). The THz frequency spectra lie between 0.1 and 4.0 THz range. The terahertz spectroscopy system (Toptica TeraFlash) is designed such that reduces the discrepancies araised by the curved surface because it has a small angle of incidence of approximately 8 (degree), which helps to maintain a relatively consistent interaction between the THz waves and the curved surface. Furthermore, the system’s focal spot size is of the order of 2.5 mm which allows for better interaction with the surface and reducing distortions (Scattering losses) caused by surface irregularities. These design considerations enable us to improve the reliability and precision of THz reflectance measurements on curved surfaces such as eggshells. The micron-level positioning accuracy between the reference pulse (reflected from a gold-coated mirror) and the sample pulse (reflected from the egg surface) is achieved using a PI motorized stage ( Physik Instrumente). The vertical precise control using pitch of micro-meter ensures consistent and optimal alignment in the terahertz reflection geometry. Furthermore, any residual misalignment between the reference and sample pulses is effectively corrected using the Maximum Entropy Method (MEM), which enhances spectral accuracy by compensating for phase and amplitude discrepancies introduced by slight positioning errors.

An algorithm written in Python was used to automatically calculate the distance between the first two peaks in the frequency domain. THz time-domain signal reflected from the gold-coated mirror E_ref is considered as the reference signal and THz signal reflected from the sample is considered as E_sam. The time-domain signal was transformed into the frequency domain by performing a Fast Fourier Transform(FFT). The complex ratio of the signals is shown below²⁹.

1

Where ‘’ is amplitude ratio and ‘’ Is the phase difference between the sample and the reference?

The real part of the refractive index , the imaginary part of the refractive index (extinction coefficient ) and absorption coefficient  is related to the amplitude ratio and phase difference as follows^30,31

2

3

The absorption coefficient in cm⁻¹ is related to the extinction coefficient is as follows

4

Where ‘c’ is the velocity of light, ‘υ’ is the frequency in the THz region.

The complex dielectric constant is related to the complex refractive index as follows.

5

From which real and imaginary values of dielectric constants can be found.

6

The real part of the dielectric constant is

7

The imaginary part of the dielectric constant is

8

Results and discussion

This section is divided into four parts. (i) The First part deals with thickness measurement and surface morphology of Fertile and infertile Eggshells. (ii) Part two deals with the systematic analyses of time/frequency spectra of eggshells to ascertain the thickness. (iii) Subsection 3 covers the measurements of the refractive index and absorption coefficients of eggshells using frequency domain spectra (iv) Part 4 deals with the measurement of real and imaginary parts of dielectric constants between 0.1 and 3.0 THz range.

Figure 1(a & b) shows the FESEM cross-section image showing the thickness of fertile chicken eggshell and eggshell membrane.

Fig. 1.

(a and b) Shows the FESEM cross-section images of chicken eggshells and membranes. The texture and thickness of both the parts are different. It also confirms that the thickness of the eggshell is much higher than the shell remembrance. The micrographs were recorded at 100x magnifications. Based on the resolution line the thickness of remembrance is of the order of a few microns whereas shell thickness is of the order of 0.3–0.4 mm.

Similarly, Fig. 2 (a and b) shows the FESEM cross-section images of chiken’s eggshells and remembrance. The texture and thickness of both the parts are very different. It also confirms that the thickness of the eggshell is almost similar to the remembrance. The micrographs were recorded at 100x magnifications. Based on the resolution line the thickness of the shell and membrane is of the order of few microns.

Fig. 2.

(a & b) Shows the FESEM cross-section image showing the thickness in micrometers of table eggshell and eggshell membrane.

The images of fertile eggshells and membranes are well-organized and smooth as compared to the table egg sample. In the next step, we recorded the time/frequency domain signals of 12 numbers of egg samples and analyzed the location of the time domain signal on the picoseconds scale and their corresponding frequency cut-off range based on Fast Fourier Transform (FFT) of recorded time domain signal. The recorded spectra provide significant information about the change in the physical and chemical changes that occurred in the table and fertile eggs. Figure 3a shows the time-domain THz signal of six numbers of chicken table eggs while Fig. 3b shows the corresponding frequency domain spectra recorded using Fast Fourier Transform (FFT) of time-domain signals of Fig. 3a. It is seen that the time domain spectra of table eggshells are located at 15ps and 12.5 ps range and their dynamical THz frequency cutoff range is around 4.5 THz range. Figure 4a shows the time-domain THz signal of six numbers of chicken’s fertile eggs while Fig. 4b shows the corresponding frequency domain spectra recorded using Fast Fourier Transform (FFT) of time-domain signals of Fig. 4a. It is observed that time domain spectra of fertile eggshells located at 11.5 ps range which is almost common for all six numbers of egg samples. However, their dynamic frequency cutoff range is around 4.0 THz. Both the time/frequency domain curves established the variation in the optical path length of the Thz signal due to variations in the thickness and refractive index of the shell.

Fig. 3.

(a-b) Chicken table eggs time domain and frequency domain spectra.

Fig. 4.

(a-b) Chicken fertile eggs time domain and frequency domain spectra.

Using the time/frequency domain signals and Phase information the refractive index of table and fertile egg samples are calculated. Figure 5(a, b) shows the refractive indices of the Table and Fertile egg samples THz frequency. The value of R.I. of the table egg sample varies between the 1.4 to 2.7 range which has the highest value at the 1.0 THz frequency range. However, R.I. values of fertile eggs lie between 2.3 and 1.5 THz range and show linear behaviour between 1.0 and 3.0 THz range. These data confirm the crystalline nature of the eggshell and the reduction in R.I. values of fertile eggs are indicators of chemical and physical changes.

Fig. 5.

(a & b) Shows the refractive indices of Table and Fertile eggs in 0.1THz- 3.0THz.

It is interesting to note the variation in the value of R.I. between 0 to 1.0THz range. It is important due to two reasons (i) The phase remain intact with the temporal curve (ii) The R.I. between 0.1to 0.3 THz range shows fluctuation due to ultrafast rise time of ultrashort pulses.

When THz waves propagate at each interface—the air-shell, shell-membrane, and membrane-albumen interfaces—of an intact egg. The crystalline CaCO3 structure of eggshells comprises mamillary cones and palisades³². A distinct, soft membrane known as the shell membrane, which is made of fibril protein and thin layers of albumen, covers the interior of the eggshell. The low absorption of the dry materials results in low attenuation of the terahertz pulse. Stated differently, the degree of attenuation is mostly determined by the water content of the medium. The material’s extinction coefficient (k) and refractive index (n) determine the strength of the transmitted and reflected pulses. The refractive index in the terahertz range is influenced by the material’s moisture content and degree of compactness, such as density and crystallinity. When light passes through a medium with a higher refractive index, it will reflect more light and move more slowly. The extinction coefficient of eggshells is much lower than egg albumen, indicating that the transmitted part of the terahertz pulse is largely absorbed by the egg white and attenuated soon. The intensity of the incident THz pulse decreases with increasing depth from the surface, as part of the incident THz pulse is reflected and absorbed by the mediums. Therefore, the reflected THz pulse intensity should be stronger from the shell-membrane interface than from the membrane-albumen interface²². Variations in intensity only influence the amplitude of the signal, not the oscillation phase of the interference signal. The refractive index of the shell membrane should also be high due to its collagen fibril content and tendon-like polypeptide structures. Separating the shell membrane with available devices is difficult, so a laser with a shorter pulse width is necessary.

The absorption coefficient is one of the important optical parameters that provide information about the transmission of the sample in the optical region. Figure 6(a, b) shows the Absorption coefficients with respect to the THz frequency of Table and Fertile egg samples. It is measured using Eq. 3. The values of Absorption coefficients for table eggs vary between 0 and 15 cm⁻¹ range whereas for fertile eggs it is between 0 and 11 cm⁻¹ range. Initial values below 0.5 THz range for both types of egg samples are almost equal but after that one can see a significant variation in the absorption coefficients of table and fertile egg samples. These notable differences between fertile and table eggshells might be due to differences in protein composition, and water content.

Fig. 6.

(a & b) Shows the absorption coefficient of Table and Fertile eggs in 0.1THz- 3.0THz.

The real and imaginary parts of dielectric constants are the very important parameters of a given sample. There are two important mechanisms associated with the dielectric medium (i) the Drude mechanism that accounts for the transport properties of free charge carriers in the material (ii) Debye relaxation are dominant process that governs the dielectric properties of solids at low-frequency regions below the microwave band. Secondly, at the higher frequency side, the mid-IR range or above the optical properties are attributed to lattice and optical phonon resonances, but the low energy tail of the spectrum is the major source of absorption. This is also known as Deby relaxation of vibrational modes in the THz range.

The real part of the dielectric is shown in Fig. 7(a, b) respectively. Similarly, the imaginary part of the dielectric constant is related to the relative permittivity of the sample. It also helps to explain the dielectric property of the material under the influence of low and high frequency due to the electronic and dielectric polarizability of the samples. Figure 8(a, b) shows the imaginary part of dielectric constants up to 7.5 to 2.5 range for table eggshells while it has 5 0.0 constant values for the fertile eggshells.

Fig. 7.

(a, b) Shows the real part of Dielectric constants for THz frequency of Table and Fertile egg samples.

Fig. 8.

(a, b) Shows the imaginary part of Dielectric constants with respect to THz frequency of Table and Fertile egg samples.

In the next step, we have focussed our attention on the THz pulse reflected from the eggshell. When a THz pulse is directed toward the egg: the first signal is obtained from the air-outer eggshell, and the second one is from the inner shell membrane. Two separate reflection peaks can be seen in the time-domain signal when a THz pulse is reflected from the egg, the first is from the air-outer eggshell, and the second is from the inner shell membrane. The composition, and thickness of the eggshell influence this oscillation. Due to variations in the medium of the inner shell i.e. the effect of remembrance reduces the amplitude of the second signal. The distance between two oscillatory peaks of the time-domain signal is proportional to the eggshell thickness³³. The major pigment in eggshells of brown-egg-laying hens is protoporphyrin IX, but traces of biliverdin and its zinc chelates are also present³⁴. Protoporphyrin IX is an organic compound that belongs to a group of biologically active tetrapyrrole compounds, with our method, it does not interfere with the precise measurement of shell thickness in brown eggs.

The thickness of the eggshell is measured as

9

Where c is the speed of light,  is the time delay between the two reflected signals and n is the refractive index of the eggshells.

Figures 9 and 10 show the difference between amplitude and time gap between table and fertile eggs. The value of Δt varies from table egg to fertile egg samples. The reflectivity from the first surface of the egg sample for table eggs is also lower than that of fertile eggs. Secondly, the time duration gap between the first and second signals in table eggs is ~ 5ps while for fertile eggs it is of the order of ~ 5ps. Moreover, the strength of the second signal is very weak in the case of fertile eggs.

Fig. 9.

Shows the separation of two numbers of THz signals in time scale. The first peak signal is from the outer shell and the second is from the inner shell.

Fig. 10.

Shows the separation of two numbers of THz signals in time scale. The first peak signal is from the outer shell and the second is from the inner shell.

The thickness in TH_Z-TDS is the ratio of peak difference to the refractive index of the material. The calculated thickness of the samples is presented in Tables 2 and 3. The measured shell thickness lies between the 0.44 to 0.33 mm range for chicken eggs, verified with FESEM. The thickness measured by FESEM ranges from 0.42 to 0.37 mm. Since THz-based measurement is based on optical path length variation in terms of wave propagation time from the outer and inner surface measured in the picoseconds range.

Table 2.

Comprises the thickness measurements of table eggshells and fertile using TH_Z-TDS.

Sl.No.	Normal egg	Thickness(mm)	Fertile egg	Thickness(mm)
1	Egg 1	0.39	Egg 1	0.41
2	Egg 2	0.36	Egg 2	0.35
3	Egg 3	0.44	Egg 3	0.37
4	Egg 4	0.39	Egg 4	0.34
5	Egg 5	0.36	Egg 5	0.38
6	Egg 6	0.37	Egg 6	0.37

Table 3.

Comprised A Pro and Cons comparative analysis of different techniques.

Method/Technique	Accuracy	Non-Destructive	Suitability for thin eggshells	Speed	Limitations	Simultaneous Measurement of (n, α, ε’, ε’’, σ)?	Cost	Reference
Micrometer Screw (mechanical)	High accuracy (± 1 μm)	No	No	Slow	Requires drilling, and treated as destructive technique	No	Economical	Portugal et al., (2012)5
Ultrasound (Acoustic Method)	Moderate accuracy	Yes	Not suitable for thin shells	Fast	Poor resolution for very thin shells, water coupling also needed and require impedance matching and may not accurately capture the adhesion status between the thin film and substrate;	No	Economical	Voisey & Hamilton, (1976)8
Optical Coherence Tomography (OCT)	High	Yes	Not suitable	Moderate	Limited penetration capability, difficult for fragile shells	No	Expensive	Sabuncu & Akdoğan, (2014)35
X-ray Micro-CT Scanning	Very High (± 0.1 μm)	Yes	Yes suitable for thin shells also	Slow	Expensive, high radiation exposure and hazardous.	No	Expensive	Maurer et al., (2015)1
Magnetic Hall Effect (HETG)	High (± 5 μm)	Yes	Yes suitable for thin shells too	Fast	It requires calibration, not suitable for fragile eggs	No	Economical	Santolo, (2018)10
Cross-section SEM	± 1 μm	No	Yes	Slow	Requires sample coating	No	Expensive	Maurer G (2012)5
Terahertz Time-Domain Spectroscopy (THz-TDS)	High (± 10 μm)	Yes	Yes	Fast	Sensitive to water molecules and need supply of dry air during experiment.expensive	Yes	Expensive	Khaliduzzaman et al. (2020)28

Thickness measurements were conducted at different positions across different eggs, with each measurement representing an average of 60 terahertz pulses. This averaging approach helps to compensate for local variations and inconsistencies in surface structure, ensuring more reliable and representative data across different measurement positions. It is to be noted that femtosecond optical pulses at 80 MHz frequency were used to generate these THz pulses. The bar diagrams of Fig. 11 (a, b) clearly show the variation of thickness of Table and Fertile eggs. The standard deviation in thickness among the Tabled and Fertile eggs are of the order of ± 0.027 and ± 0.022, respectively.

Fig. 11.

(a, b) Shows the comparative histograms of Tabled and Fertile eggs.

Table 3 provides a brief but multiple parameters based pro and cons analyses of different techniques used for measurement of thickness and other physical parameters.The table also comprises corresponding references for easy review.

Conclusions

We have demonstrated the use of Time-domain THz spectroscopy for the characterization of optical properties of Table and Fertile Chicken’s eggshell. In addition, the optical technique to measure the thickness. Time/frequency domain spectra data were recorded between 0.1 and 3.0 THz range. R.I., absorption coefficients, and real and imaginary parts of the dielectric constants were measured. It was noticed that values of R.I. of table eggs at 0.8 THz were higher than 2.5 as compared to fertile eggs. Similarly, the absorption coefficient values for infertile eggs lie between 2 and 14 cm⁻¹ compared to fertile eggs, which lie between 2 and 10 cm⁻¹ range. The most important aspect of our study covers the measurements of real and imaginary parts of dielectric constants between the 1.2 to 3.0 THz range the infertile eggs show a steep drop in values between 4 − 2.0 range while fertile eggs show an almost linear response of 4 0.0 in the given frequency range. The imaginary parts show infertile egg values between 7.0 and 3.75 while fertile eggs show a consistent result of the order of 5.0. This study will significantly contribute to non-invasive in-vivo research as well. The ability to differentiate fertile eggshells from infertile eggs demonstrates the versatility and capability of terahertz spectroscopy in enhancing our understanding of biological samples.

Author contributions

The author JI, involved in experimental data collection, planning and analysis and first revised darft of manuscript; NP, for dedicated THz experimental data collection, data analyse,writing and revision of the manuscript. Both JI and NP  have contributed equally; AB, reseach plan proposal, conceiving the idea, first draft preparation; AKC, conceving the idea of execution, THz experimental arrangement, project garnts, analyses and prepration of first and final draft of the manuscript; KAJ, conceiveing the research idea, first draft prepration; RP, Egg samples collections, monitoring the quality and standard and scientic discussion.

Data availability

The datasets generated during and/or analysed during the current study are not publicly available due to ongoing rapid data collection and research in this field by the group but are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.