Title of My Thesis - RAIITH - IIT Hyderabad

Optical microscopic techniques

Introduction

He termed it 'holography' from the Greek words 'halos' meaning whole or whole and 'graphein' meaning writing. A hologram is the photographically recorded interference pattern between a wave field scattered from the object and a reference wave, which is a coherent background. The data is encoded in the form of interference patterns, which contain high spatial frequencies and cannot be seen by human eyes.

Reconstruction of the image is performed by re-illuminating the hologram with a reference wave. The further development of holography was hampered for several years after its invention due to the unavailability of coherent sources. In 1967, the first hologram of the person was created, paving the way for a specialized application of holography.

Benton invented white light transmission holography in 1968, which allows the hologram to be viewed in plain white light, creating a rainbow image from the seven colors that absorb white light. Schnars and Juptner developed direct recording of Fresnel's holograms with charged coupled devices, revolutionizing the field of holography[18], [19].

Holography

Recording and Reconstruction

In order to reconstruct hologram, amplitude transmission is multiplied by complex amplitude of the reference wave.

Image Equations

The corresponding point of the real and virtual images is equidistant from the hologram plane, but on the opposite side of it.

Digital Holography

General Principles

In reconstruction, the virtual image is displayed at the position of the original object and the real image at distance d in the opposite direction as shown in Figure 2-6. 𝐸𝑅 = 𝑎𝑅+ 𝑖𝑜 = 𝑎𝑅 (2. 21) The diffraction pattern is calculated behind the CCD plane at a distance d, it reconstructs the complex amplitude in the plane of the real image. Since the reconstructed wavefield is Γ( 𝜉′, 𝜂′) is a complex function, both intensity as well as phase can be calculated[22].

The lens is located directly behind the hologram in simple cases, as shown in Figure 2-9.

Off-axis holography

The third term gives the reconstructed virtual image and the last term gives the real conjugate image. Therefore, the spectrum of the virtual image can be isolated provided that the off-axis angle 𝜃 is large enough.

Figure 2-11 : Reconstruction setup for off-axis [15]

Numerical Reconstruction

Reconstruction by the Fresnel Approximation

The interesting property of the hologram is that each part of the hologram contains information about the entire object. This is illustrated in Figure 2-15 and Figure 2-16 with the black mask covering almost half of the area[13].

Reconstruction by convolution approach

Δ𝜉 = Δ𝑥; Δ𝜂 = Δ𝑦 (2. 36) Reconstructing holograms using the convolutional approach results in images with more or fewer pixels per unit length than those reconstructed using the Fresnel approximation. The convolutional approach is advantageously used to reconstruct in-line holograms from particle distributions in a transparent medium.

Digital Fourier Holography

Separation of DC-term

Introduction

Optical setup

In-line hologram formation

Reconstruction techniques

Image recovery by optimization

Image recovery by simulating the physical hologram replay process
Image recovery by spatial filtering approach
Image recovery by solving minimum L2-norm problem
Image recovery by solving minimum L2-norm problem

A spatial filter of larger size can improve the image resolution as shown in Figure 3-4 (b), but the restoration has interference from the dc term which causes the introduction of speckle noise that obscures the high resolution features. For an even larger filter pixels as in Figure 3-4 (e), the corresponding reconstruction in Figure 3-4 (f) is completely obscured by contribution from the dc term. Thus, the useful resolution did not improve due to the speckle artifacts and/or obscuration due to the dc term when increasing the filter window size.

Quadrature filters are used here, any windowing on the filters is not expected to solve the DC-term interference problem in this type of approach[49]. Image restoration by solving minimum L2-norm problem Without smoothing operation, the iteration can be described by Without smoothing operation, the iteration can be described by. The relative L2 norm error is seen to decrease less than 0.1% in successive iterations when 20 iterations are reached.

Although the iterative solution provides a minimum L2-norm solution for the complex field 𝑂(𝑥, 𝑦) from a single hologram frame, the solution is modulated by the carrier fringes and their harmonics. The modulation on the solution must be balanced in the iterative process to achieve the desired solution, which we show next. The carrier fringe period in the recorded hologram (Figure 3-2 (a)) corresponded to 24 pixels on our CMOS array detector.

Further, there is no interference from the twin image or dc terms and as a result the high frequency features in the resolution plot are much more clearly visible.

Figure 3-3 : Image recovery by simulating the physical hologram replay process[49]

Iterative Method

Here, the first is obtained by calculating the slope of the intensity in direct reconstruction with the Sobel edge detector [51]. If the internal support 𝑈𝑟𝑛(𝜉, 𝜂) is negative due to interference between the reference wave and the twin image, the corresponding point 𝑈𝑟𝑛(𝜉, 𝜂) is increased during iterations until all points inside S become negative [52]. e) 𝑈𝑟𝑛(𝜉, 𝜂) expands to form a new complex field 𝑈ℎ𝑛(𝑥, 𝑦) on the recording plane. In in-line holography, the angle between the object wave and the reference wave is zero, which distinguishes it from conventional off-axis holography.

The larger the angle is, the better the separation between the DC term, the real image and the virtual image in the FFT will be. Thus, reconstruction can be easily achieved in off-axis holography, but optimization is required in line holography. If the off-axis angle in off-axis holography is reduced to zero, it will lead to in-line holography, so we started with an off-axis holography simulation where the off-axis angle was 20 and then reduced it to 0.20.

Simulations

In another simulation, hologram (Figure 4-14) of object "H" (Figure 4-11) is created through the simulation with the reference beam at an angle of 0.20 to the object beam as shown in Figure 4-12 and reconstructed using optimization technique. The FFT of the hologram before optimization is shown in Figure 4-14, It contains all terms, ie. DC, virtual and real term, and the extent of overlap seen is more compared to the above case, the image is restored by optimization, FFT only shows virtual term Figure 4-18, therefore optimization has a big influence when the off-axis angle is smaller.

Figure 4-1 : “H” Object Figure 4-2 : Reference wave illuminated at 2 0

Off-axis holography

Object reconstruction is done by multiplying the reference wave with the hologram and propagating the wave field in the image plane using Fresnel propagation.

Results

In-line Holography

Optical setup

Practical In-line hologram Reconstruction

The hologram of the image is shown in Figure 4-41 and is FFT in Figure 4-42. It clearly contains an overlap of all components, i.e. DC, virtual image and real image. The “Digital holography microscopy (DHM) is an optical microscopic principle that allows the hologram to be captured optically and the object to be digitally reconstructed. In lens-free in-line holography, the laser source is replaced by partially coherent LED to obtain the same results with reasonable accuracy.

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