Microscope Phase Contrast Calculation: A Comprehensive Guide

Microscope phase contrast calculation involves the measurement of the phase variations of optical sections of samples, which can be achieved using a quantitative phase-contrast confocal microscope (QPCCM). The QPCCM combines a line-scanning confocal system with digital holography (DH) to merge the merits of these two different imaging modalities, providing high-contrast intensity images with low coherent noise and optical sectioning capability, as well as access to phase profiles of the samples.

Understanding the Principles of Microscope Phase Contrast Calculation

The phase contrast microscopy technique is based on the principle of converting phase differences in the specimen into brightness differences in the image. This is achieved by introducing a phase shift in the undeviated (or direct) beam relative to the diffracted beam, which results in the interference of these two beams and the creation of a phase contrast image.

The phase contrast calculation can be expressed mathematically as follows:

I = I₀ + 2√(I₀I₁) cos(Δφ)

Where:
– I is the final intensity of the image
– I₀ is the intensity of the undeviated (direct) beam
– I₁ is the intensity of the diffracted beam
– Δφ is the phase difference between the direct and diffracted beams

The key parameters in this equation are the phase difference Δφ and the relative intensities of the direct and diffracted beams, I₀ and I₁, respectively. By manipulating these parameters, the phase contrast can be optimized for different types of samples and imaging requirements.

Quantitative Phase-Contrast Confocal Microscope (QPCCM)

The QPCCM is a powerful tool for microscope phase contrast calculation, as it combines the advantages of both confocal microscopy and digital holography. The main components of a QPCCM system are:

1. Confocal Microscope: The confocal microscope provides high-contrast intensity images with low coherent noise and optical sectioning capability.
2. Digital Holography (DH): The DH component allows for the measurement of the phase profiles of the samples, providing quantitative information about the sample’s structure and properties.

The integration of these two imaging modalities in the QPCCM system enables the following key features:

Lateral and Axial Resolution

The measured lateral and axial resolutions of the intensity images from the current QPCCM system are approximately:
– Lateral resolution: ~0.64 μm
– Axial resolution: ~2.70 μm

These high-resolution capabilities allow for the detailed analysis of microscopic samples.

Phase Measurement Precision

The noise level of the phase profile measured by the QPCCM is around ~2.4 nm, which is better than the result obtained by DH alone. This high precision in phase measurement enables the quantitative assessment of height variations in samples, as demonstrated in Fig. 6(l) of the referenced paper, which shows the height variation of a focused surface.

Quantitative Phase Profiles

The QPCCM can obtain quantitative phase profiles at a better noise level than DH, making it suitable for a wide range of applications, including:
– Industrial inspection
– Biomedical imaging

Numerical Compensation and Adaptive Optics

The QPCCM also opens up avenues for the development of various numerical compensation methods and a full digital adaptive optics system, particularly for biomedical imaging applications, such as ophthalmic imaging.

Applications and Examples of Microscope Phase Contrast Calculation

The QPCCM has been successfully applied in various research and industrial settings, demonstrating its versatility and capabilities. Here are a few examples:

Quantitative Phase Imaging of Paramecia

Zhang et al. (2020) developed a polarization grating-based diffraction phase microscopy system for quantitative phase imaging of paramecia. The system was able to capture the phase profiles of the paramecia with high precision, allowing for the analysis of their morphological changes and dynamic behavior.

Transmission Structured Illumination Microscopy

Wen et al. (2021) presented a transmission structured illumination microscopy (tSIM) technique that combined quantitative phase and scattering imaging. This approach enabled the simultaneous acquisition of high-resolution intensity, phase, and scattering information, which was useful for the characterization of biological samples.

Ophthalmic Imaging

The high precision and low noise level of the QPCCM make it a promising tool for ophthalmic imaging applications, such as the assessment of corneal and retinal structures. The integration of adaptive optics can further enhance the imaging capabilities, allowing for the correction of aberrations and the visualization of fine details in the eye.

Numerical Examples and Calculations

To illustrate the practical application of microscope phase contrast calculation, let’s consider a specific example:

Suppose we have a sample with a refractive index of 1.33 and a thickness of 10 μm. We want to calculate the phase difference between the direct and diffracted beams.

Given:
– Refractive index of the sample: n = 1.33
– Thickness of the sample: t = 10 μm

The phase difference Δφ can be calculated using the following formula:

Δφ = 2π(n - 1)t / λ

Where λ is the wavelength of the illumination light.

Assuming a wavelength of 532 nm, the phase difference can be calculated as:

Δφ = 2π(1.33 - 1) × 10 × 10^-6 / 532 × 10^-9
   = 0.0395 rad

This phase difference of 0.0395 rad (or approximately 2.26 degrees) can then be used in the phase contrast calculation equation to determine the final intensity of the image.

Conclusion

Microscope phase contrast calculation is a crucial aspect of quantitative phase imaging, enabling the detailed analysis of microscopic samples. The QPCCM, which combines confocal microscopy and digital holography, provides a powerful tool for this purpose, offering high-resolution intensity images, precise phase measurement, and the ability to quantitatively assess sample properties. The applications of this technology span various fields, from industrial inspection to biomedical imaging, and the continued development of numerical compensation methods and adaptive optics will further enhance its capabilities.

References

1. Liu, C., Marchesini, S., & Kim, M. K. (2014). Quantitative phase-contrast confocal microscope. Optics Express, 22(14), 17114-17125.
2. Zhang, M., Ma, Y., Wang, Y., Wen, K., Zheng, J., Liu, L., & Gao, P. (2020). Polarization grating based on diffraction phase microscopy for quantitative phase imaging of paramecia. Optics Express, 28(18), 29775-29787.
3. Wen, K., Ma, Y., Liu, M., Li, J., Zalevsky, Z., & Zheng, J. (2021). Transmission structured illumination microscopy for quantitative phase and scattering imaging. Frontiers in Physics, 8, 630350.