Problem 9.1 Phase Contrast Microscopy.
(a) A phase contrast microscope is used to observe a transparent biological cell that introduces a phase shift of radians. Assuming small phase approximation, calculate the intensity variation observed in the image compared to the background.
(b) Explain why a standard bright-field microscope cannot image a pure phase object. What modification does the phase contrast microscope introduce to solve this problem?
Problem 9.2 Confocal Microscopy.
(a) A confocal microscope uses a pinhole of diameter 50 μm placed in a conjugate image plane. If the objective has a magnification of 60× and a numerical aperture of 1.4, estimate the effective resolution improvement compared to conventional microscopy.
(b) Describe how the pinhole in a confocal microscope improves both lateral and axial resolution. What happens to the signal intensity as the pinhole size decreases?
Problem 9.3 Fluorescence Microscopy.
(a) A fluorescent molecule (GFP) has an excitation wavelength of 488 nm and an emission wavelength of 509 nm. Calculate the Stokes shift in both wavelength and energy.
(b) Explain the role of the dichroic mirror in a fluorescence microscope. Why is it essential for separating excitation and emission light?
Problem 9.4 Scanning Near-Field Optical Microscopy (SNOM).
(a) A SNOM probe has an aperture of 50 nm. Estimate the theoretical resolution achievable with this probe when imaging a sample at visible wavelengths (~500 nm). Compare this to the diffraction limit of a conventional microscope with NA = 1.4.
(b) Explain the difference between collection mode and excitation mode SNOM. What are the advantages and limitations of each configuration?
Problem 9.5 Resolution Limits.
(a) An optical microscope has a numerical aperture of 1.3 (oil immersion) and operates at λ = 550 nm. Calculate the Rayleigh resolution limit.
(b) A confocal microscope is claimed to have 1.4× better lateral resolution than a conventional microscope. Justify this claim using the point spread function properties of confocal imaging.