Development Of Pdi Plates For Industrial Applications Biology Essay

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Due to rapid development in the field of photonics and optical communication, various measurement techniques are developed using the properties of laser. Research is also in progress to apply these tools and techniques in the real world commercial scenarios. One of these scenarios is surface roughness measurements with the help of non-contact methods. In this regard, our work is concerned with the development of point diffraction interferometer plates for industrial application of point diffraction interferometry in surface roughness measurement.

We would like to express our deep gratitude for Professor Lars Bååth for providing us with this opportunity and his continuous support and suggestions for the design of PDI plates. We are also very grateful to Ms Sameera Atraqji, Ph.D. student under our supervisor, for her great support in all aspects.. We are also thankful to Mr. Bengt Nilsson, MC2 lab, Chalmers University of Technology for turning our design into reality by fabricating these plates.

Abstract

The aim of this Master's Degree thesis project is to design and develop point diffraction interferometer plates. In this project the PDI plates are re-designed, changing the design which was used in previous projects in Halmstad University. The transparency of PDI plates can be controlled by coating them with NiCr film. Firstly, four plates with coating of different thickness of NiCr were developed. The relationship between transmittance and the thickness of NiCr was established by testing these plates for transmittance and reflectance with the help of a laser and an optical power meter.

The absorption coefficient of clear substrates and reflection of light is also taken into account to achieve the correct results. The parameters like the diameter of semi-transparent area around the pinholes and the size of pinholes is chosen after fully understanding its application. The lay-out and description of design is also included in the report.

Abbreviations

PDI

Point Diffraction Interferometer

NiCr

Nickel Chromium (Nichrome)

T

Transmitted intensity

α

Absorption Coefficient

x

Thickness of metal film coating

λ

Wavelength

I0

Intensity of Incident light

I1

Intensity of light passing through NiCr

I2

Intensity of light passing through glass substrate

Ix

Intensity of Transmitted light

IR1

Reflected intensity at Air-NiCr interface

IR2

Reflected intensity at NiCr-Glass interface

IR3

Reflected intensity at Glass-Air interface

α1

Absorption Coefficient of NiCr

α2

Absorption coefficient of glass

x1

Thickness of NiCr Coating

x2

Thickness of Glass substrate

B

Constant

IR

Reflected intensity

R

Ratio between Reflected intensity and Incident intensity

A

Absorbed Intensity

C

Transmitted intensity + Absorbed intensity

T1

Transmittance calculated in first experiment

T2

Transmittance calculated in second experiment

f#

Ratio between focal length and the diameter of entrance pupil

Contents

Preface _1842612680"i

Abbreviations _1842612680"iii

Contents _1842612680"iv

1 _1842612680"Introduction _1842612680"1

2 _1842612680"PDI Interferometer System _1842612680"3

3 _1842612680"PDI Plates _1842612680"6

4 _1842612680"Fabrication Process _1842612680"14

5 _1842612680"Experiments with semi-transparent plates without holes _1842612680"21

6 _1842612680"Conclusion _1842612680"31

7 _1842612680"References _1842612680"32

List of Figures

1 Introduction

In today's world where technological advancements are achieved in rapid succession, there is intensive study in progress to develop microscopic mechanical components which will reduce the size of normal devices to nanometer scale. For this purpose one of the most important requirements is to have very smooth metallic surfaces which have to be used in these mechanical systems. The roughness on these surfaces is so small that it is very difficult to measure it through conventional surface roughness measurement techniques.

There are two kinds of surface roughness measurement techniques i.e. contact method and non-contact method. Contact methods are limited in terms of resolution as they have a limited size of the point contact which is touching the surface. There exists contact methods with extreme spatial resolution (down to atomic resolution) e.g. scanning probe microscopy, but these measurements are very time consuming and not suitable for investigation of large areas. That is why nowadays most of the research is focused on developing more accurate non-contact methods. One of the most widely used non-contact methods is the optical method.

There are various optical methods of which one is optical interferometry. A number of optical interferometry systems are developed and being used for surface roughness measurement, but most of the systems are either very complex in design or very costly.

Efforts are being made to make optical interferometers simpler in design and much more cost effective on the other hand improving the performance. One of these simple and cost effective systems with high performance is the point diffraction interferometer.

PDI systems are used in many other optical applications and one of them is Real-Time Flow Visualization. Julius E. Okopi has worked in this field under our Supervisor, Professor Lars Baath. Now, this same optical measurement technique is being used for surface roughness measurements for mechanical engineering uses. In this regard Sadi Khalid Abu Dalou has done his Master's thesis project. His thesis was about 3-D Imaging of Metal surfaces using Point Diffraction Interferometry. There is a PhD project in progress under our supervisor in which Ms. Sameera Atraqji is working on the development of Hand-held Surface roughness measurement equipment based on Point diffraction Interferometry.

The PDI system was proposed and developed by R N Smart in 1972 [6]. The main component of PDI systems is the PDI plate. Previously PDI plates were developed during Okopi's project in 1992. Now, however, these plates are showing signs of wear and tear and also the readings are no longer reliable. So our project is to re-design and develop these plates and get these plates fabricated. The plates were fabricated at MC2 labs at Chalmers University of Technology.

1.1 Goals

The objective of this thesis project is to develop and fabricate the PDI plates for industrial applications. For this purpose, we have analyzed the transmittance through the PDI plates, the reflection of light and absorption coefficient of the material. Initially, the transmittance through simple, semi-transparent plates was analyzed, which becomes the basis of the thickness of NiCr to be coated during the fabrication process.

2 PDI Interferometer System

There are many experiments being performed, in different fields, using the point diffraction interferometer system. Here we will discuss the concept and working of point diffraction interferometer in the field of surface roughness measurement by imaging the surface and analyzing the image.

2.1 Theory

The instrument which measures the variation of phase across a wave-front by interfering with the object beam and reference beam is called an "interferometer". In this project, we are specifically using point diffraction interferometry.

The small deformations in the metal surface can be easily measured by the interferometers. Although many interferometry methods are in use, one of the most commonly used and most precise method is point diffraction interferometry. Common path interferometers are free from environmental limitations. As they are using a common path design, they are insensitive to the vibrations in optical path.

Figure : Light waves through PDI Plate [2]

The point diffraction interferometer is based on common path interferometry. Both the reference and object beams are transmitted along the same path. An object wave front is generated. When any point discontinuity is created in the path of object wave front, there will be a change in the phase of the object wave-front. Both of these beams will interfere with each other when they pass through the pinhole, according to the diffraction effect. They will create a light intensity pattern called an "interferogram", which can be observed and analyzed for further use [7].

2.2 Setup and working of Point Diffraction Interferometer system

Although different setups have been used in previous applications of PDI systems, we are going to use the same configuration used in the previous Thesis of Mr Sadi Khalid Abu Dalou[2].

The laser beam passes through a beam expander. From the beam expander, the beam passes through beam splitter and one part of the beam is directed towards the focusing lenses and the other part is directed towards test surface. The beam, which strikes the test surface, reflects back towards the focusing lens and through the PDI plate. This beam is called the "object beam" [5].

There will be a phase change in the wave front of the object beam as it strikes on the test surface. When these beams pass through the PDI plate, the result is that they interfere with each other. After the PDI plate, the light beam, which consists of a reference beam and an object beam, creates a light intensity interference pattern, called an "interferogram", and which is collected on to a recording medium. In our case, the recording medium is a CCD camera.

Figure : Point Diffraction Interferometer System [2]

The most important part of the PDI system is the PDI plate. It is constructed as follows. The PDI plate is made from a clear substrate, and it is coated with a thin metal film to make it semi-transparent. The thickness of the metal film determines the transmittance of the semi-transparent area. The last step is to make a Pinhole in the centre of the Semi-transparent area which creates a point discontinuity in the path of the incident wave-front. The whole fabrication process is described in detail in section 4 of this report.

3 PDI Plates

3.1 Overview

The core component of point diffraction interferometer is the PDI plate. The PDI plates are used to let the phase beam and reference beam interfere, with the help of the phenomenon of diffraction of light. "When a beam of light is focused on the pinhole as depicted in figure 3, a small portion of light passes through the pinhole to generate a spherical wave-front, while the remaining portion of the incident light is transmitted through the semi transparent coating. The transmitted wave-front has the same phase as the incident wave, but its amplitude is attenuated. The degree of attenuation is determined by the optical density of the plate. A Point Diffraction Interferogram which is observed at the image plane, is formed as a result of the interference between the transmitted wave-front and the spherical wave-front." [1]

Figure : Fringe formation using PDI plate [1]

The transmittance of light through point diffraction interferometer plates depends upon various parameters e.g. thickness of the NiCr coated on it, the absorption coefficient of the NiCr, the absorption coefficient of glass and the reflection of light. To design the point diffraction interferometer plates, all parameters should be taken into account. In this section, we have taken an overview of all parameters for an efficient design of point diffraction interferometer plates.

3.2 Parameters for design of PDI plates.

For an efficient design of a point diffraction interferometer, the parameters like thickness of the metal film coated on it, the absorption coefficient of material, reflection of light from the surface of point diffraction interferometer plates and the diameter of the pin-hole and the area of the semi-transparent circular region around the pinhole are discussed.

3.2.1 Transmittance through PDI plates

As discussed earlier the transmittance of point diffraction interferometer plates depends upon the thickness of the metal film deposited on it and the absorption coefficient of the material. We can use the following expression,

Where

T=Required transmittance

=Absorption coefficient

x= Thickness of metal film coating

Here in our project, we used Nickel Chromium (NiCr) as coating material. Other materials like Gold (Au) may also be used.

3.2.2 Thickness of metal film coating

The thickness of the metal film coated on to the clear substrate is an important parameter for determining the transmittance through the point diffraction interferometer. A layer of metal, like NiCr, is deposited on the clear substrate which is used to control the transmittance. The greater the thickness of the metal film on the clear substrate, less will be the transmittance of light. Initially, simple semitransparent plates with the thickness 7.5nm, 34nm, 42nm and 60 nm for point diffraction interferometer were made just for testing purposes.

3.2.3 Absorption coefficient of material

When the light passes through the material some of the light is absorbed. It is the characteristics of the material which determines the extent to which light can penetrate through any material. When the light passes through any transparent material, due to its interaction with atoms and molecules, some of it is lost. To estimate the transmittance it is necessary to consider the absorption coefficient of material also. In our project we have measured the absorption coefficient of the material by experimenting with the test plates (semitransparent plates). The experimental set-up and measurements will be discussed in later sections.

The plates with just the semi-transparent coating were tested and the measurements were taken and the calculations were done to estimate absorption coefficient.

3.2.4 Area of semi transparent circular region

Around the pin-hole, the metal film is coated according to the desired thickness. The semitransparent region becomes opaque by depositing the metal film on it. When the light passes through it, it produces the object wave-front. The area of semitransparent circular region should be designed to be five times more than the spot size of the laser beam used. In our project we suggested this semitransparent area to be 300µm in diameter.

3.2.5 Size of pin-hole

The fabrication process of the point diffraction interferometer is finished when a circular pin-hole is etched in the middle of the semitransparent area. The size of the pin-hole depends upon the transmittance through the coating of metal film around it. A mathematical way to decide it is that it should be half the diameter of the Airy disk of the focusing lens. The Airy disk diameter of the lens is a function of F-number (f#) of the lens and wavelength (λ) of light used. It can be calculated as;

Airy diameter = 2.44 Ã- f# Ã- λ

In our project we suggested the size of pin-holes as 2.5µm, 3.5µm, 4.5µm and one without holes.

3.3 Description of proposed Design of PDI plates

In this section, details are given of our proposed design. The specifications of the design are also discussed in this section.

3.3.1 Lay-out of PDI plates

The base material used for the PDI plates is Soda-Lime mask-blank. For this purpose, we have used the 3in * 3in (75mm * 75mm) Soda lime glass plate with 100nm Chromium (Cr) coating. It is divided into four equal quarters of equal dimensions and an equal number of PDI units on each quarter. Each quarter has nine PDI devices i.e. nine circular, semi-transparent areas with a pinhole in its center. The size of all the pinholes in a single quarter is the same and the size of all the semi-transparent areas in all four quarters is same i.e. 300μm. In three quarters there are pinholes with sizes 2.5μm, 3.5μm and 4.5μm respectively, and in the fourth quarter there are no pinholes in the center of the semitransparent area. This is done in order to have a control section for testing the transparency of the plate. A rough design layout is shown in figure 4.

Figure : PDI plate design layout

3.3.2 The alignment of pin-holes

Here, we have proposed a design with point diffraction interferometer plates in four quarters where each quarter has an equal number of PDI units. There are three rows, and each row contains three point diffraction interferometers PDI units. All these units are equidistant from adjacent PDI unit. The diameters of holes suggested were 2.5µm, 3.5µm, 4.5µm and one quarter with no holes. The fourth quarter in which we have only semi-transparent areas are also aligned in the same manner as the other three quarters.

3.3.3 Size of Semitransparent area

The semitransparent area is created by coating the metal. "A good rule of thumb to use in choosing the semi-transparent region is to ensure that the area is large enough to make it visible to the naked eye and it should be a factor of 5 larger than the spot size of the laser used for the experiment."[1]

Figure : Size of semi-transparent area

3.3.4 Space between the centers of circular semitransparent area

In our project we suggested the space between centers of semitransparent areas is 5mm.This means that each semi-transparent area is 5mm apart from adjacent PDI units as shown in figure 6. This spacing is done in order to locate the PDI unit easily on the PDI plate. In the previous design the process of locating the pinhole was very difficult as it has to be located with the naked eye by passing the laser through it. Now in our design it will be easier to locate the pinhole by just mounting the plate in the rail system through which we can accurately move the plate in millimeters.

Figure : Spacing between the adjacent PDI units

3.3.5 The placement of marks

In our design, we placed the marks (+) for alignment. It will become easy to determine the exact center after fabrication, when the plate will be divided into four quarters of equal dimensions. These marks will also be useful for referencing by the lithography machine for etching the pinholes right in the centre of the semi-transparent areas. These marks are shown in figure 7

Figure : E-beam marks

4 Fabrication Process

The point diffraction interferometers plates were manufactured at the nanoscience lab MC2, Chalmers University of Technology. A basic fabrication process was used for the development of point diffraction interferometer plates. In this section, we will provide an overview of the fabrication process.

4.1 Fabrication process of Semi-transparent plates

We tested the four point diffraction interferometer plates of different thicknesses of NiCr e.g.7.5nm, 34nm, 42nm and 60nm. First these plates were fabricated in Chalmers University of Technology labs and forwarded to us for testing of their transmittance. The testing was done in Halmstad University lab under the supervision of our supervisor, Professor Lars Baath. The details of the experimental setup, measurements and calculations on the basis of these measurements are described in the next sections.

4.1.1 Coating of semitransparent material

The fabrication of semitransparent plates was done by metal coating on the clear substrate e.g. glass. Thicknesses of 34nm, 42nm, 60nm and 7.5nm of NiCr were deposited on the clear substrate. The purpose of these various thicknesses is to estimate the proper thickness, with the help of experiments, to be coated for the required 2% and 4% transmittance.

During the fabrication process first of all, all the plates were cleaned by ozone (O3), an allotropic form of oxygen, for 20 minutes. After that, one of the plates was mounted in the thermal evaporation system. 42 nm thickness of metal film (NiCr) was deposited. After removing it from the thermal evaporation system, the same process was repeated for the remaining three plates e.g.7.5nm, 34nm and 60nm.

4.2 Fabrication process of PDI plates

In this section, the complete fabrication process of PDI plates is discussed. A four inch mask was first prepared with E-beam lithography. This mask only contains empty spaces for Semi transparent areas with 300μm of Cr etched from the Cr coated Soda-Lime Mask-Blank. This plate was used as a stencil for the fabrication of the original plates. Four 3inch plates were fabricated using the four inch mask and photolithography. The purpose of making this 4 inch mask is to have a stencil which can be used to make three inch plates in large numbers. Then, these three inch plates are coated with NiCr according to the given specifications i.e. 40nm and 50nm. Finally, the pin hole is etched in the centre of each semi-transparent area. This whole process is completely described in the figures as follows.

4.2.1 Pattern preparation

The first step was to design the layout in AutoCAD. There were some restrictions for completely translating our design into practical AutoCAD design which have to be used for the fabrication. One of them was the shape of pinhole, which in our design was circular, had to be replaced by an octagonal shape. This was done, as the e-beam lithography machine is not able to write the circular shape of this size (2.5μm and etc.) with extreme precision. So the closest shape to a circular shape is an octagon and so it was replaced. Two layers were used as one layer for limiting apertures, light alignment and e-beam alignment by using a photolithography mask plate and the second layer for creating the pinholes by using the e-beam lithography. The basic design is shown in figure 9.

Figure : Pattern Preparation

Now our design in AutoCAD format was exported into the DXF (Autodesk drawing exchange) format, version R12-R14 and then it was converted to GDS pattern format. In e-beam lithography, a major difficulty is resolution; it may be limited by the scattering of electrons. When electrons hit the surface of resist they penetrate the underlying substrate and a collision occurs. This causes to lose the energy of electrons or they leave the material. This is called "backscattering". Due to backscattering, electrons can irradiate from the centre of the exposure beam of the laser. This also affects the neighboring irradiations'. This phenomenon is known as the "proximity effect" [3]. To reduce the proximity effect in the fabrication process, the pinhole layer was locked to a 50nm grid. Lastly, the GDS file was converted into JEOL51 e-beam (machine readable) format for JEOL equipment.

4.2.2 Preparation for PDI aperture photo mask

For commercial purposes, a 4-inch mask was developed before which was used as stencil or dye for fabrication of plates. A four inch soda lime mask blank was prepared with 100 nm chromium coating. The UV5 electron beam resist was spin coated at 3000 r.p.m resulting in a thicknesss of 0.8µm. The substrate was soft baked at 130C for 3 minutes on a hotplate. The reason for soft baking is to eliminate the solvent in the resist.

Figure : 4-inch Photomask preparation

Next, the file prepared for pattern in JEOL51 format was exposed in a JBX5DII electron beam lithography system, having the specifications 50KVA, 10nA, 300µm aperture, 0.25µm beam steps and 12µc/cm2 exposure dose. A post exposure bake was given to substrate at 130C for 12 minutes in the oven. After baking the substrate, MFA developer was used to develop for 60 seconds. The plates were then rinsed in water. The plates were baked in oven at 130C for 25 minutes to improve the resist adhesion. Oxygen plasma was used to clean the surface. Subsequently the plate was dipped in water and etched for 65seconds in standard mask Cr-etch. The resist was striped by using remover 1165(N-Methyl-Pyrrolidone) overnight. The whole process is described in graphical way in figure 10.

4.2.3 PDI aperture photo lithography

A 3 inch soda lime mask blank is used with 100 nm of chromium coating. By spin coating S-1813 photo resist is coated at 3000 rpm. A 1.5µm thick layer of photo resist is deposited on the plate. The substrate was allowed to soft bake at 130C for 3 minutes on the hotplate.

Figure : PDI Aperture Photo Lithography

The PDI aperture pattern is exposed onto the 3-inch plate in Karl Suss MA6 mask aligner, using the 4-inch photo mask from the previous step. This substrate is then developed for 45 seconds in MF319 developer solution. After developing the resist the substrate is rinsed in water and then etched for 75 seconds in standard Cr etch. Then the resist is removed with the Remover 1165 and rinsed with water. The graphical explanation is given in figure 11.

4.2.4 Semi-transparent layer deposition

For this step, the plates prepared in the previous step with only 300μm of Cr etched are coated with NiCr coating. The thicknesses specified in our design are 50nm and 40nm for 2% and 4% respectively. So two out of four plates are coated with 40nm NiCr and two of them are coated with 50nm.

Figure : NiCr coating in Thermal evaporation system

Firstly the plates from the previous step are cleaned in ozone for 20 minutes. Then the plate is mounted in the thermal evaporation system and 40nm or 50nm NiCr is deposited as shown in figure 12. The thickness of the NiCr coating depends on evaporation time. The plate is then removed from the system and the process is repeated for other plates.

4.2.5 PDI pin-hole E-beam lithography

To create the pinholes in the semitransparent region e-beam lithography is used. UV5 electron beam resist was spin coated at 3000 r.p.m resulting in a thickness of 0.8µm. These substrates were baked at 130C for 3 minutes. Now proximity corrected "PDI pin-hole layer "was exposed in the JBX5DII electron beam lithography system at 50KV, 0.25nA, 300µm aperture 0.05µm beam step, 12µc/ exposure dose. Mark detection is used to align the pinholes correctly in the center of the apertures as shown in figure 12.

A post exposure baking of the substrate at 130C for 12 minutes was carried out. This post baked substrate was developed for 55 seconds in MF24A developer and was then rinsed with water. This substrate is allowed to bake at 130C for 25 minutes in the oven to improve the resist adhesions. Oxygen plasma is used to clean the surface. Then again it is rinsed with water. It is now dipped in Cr-etch for 25 seconds for etching away the NiCr. Then the resist was stripped in remover 1165(N-Methyl-pyrrolidone) for one hour. After being taking out from remover it was again rinsed with water. Graphical representation of the process is given in figure 12.

Figure : Pinholes fabricated by e-beam lithography

4.2.6 Cutting of the plates

Finally, when the fabrication process was completed the plate was mounted onto a tape-ring and then placed in the Disco DAD3350 diamond saw. The 3 inch plate was divided into separate devices as shown in Figure 13.

Figure : Cutting of the plates

5 Experiments with semi-transparent plates without holes

5.1 Testing for the relationship between transmittance and thickness of NiCr.

In this part, we have studied the relationship between transmittance through point diffraction interferometer and above specified thicknesses to estimate the absorption coefficient of NiCr. This will be used in estimating the required thickness of NiCr to be deposited to get 2% and 4% transmittance.

5.1.1 Experimental setup

In our experiment, we passed the Helium Neon (HeNe) laser through the power regulator and then through the NiCr coated test plates. The transmitted intensity of light is measured by Thorlabs optical power meter. By connecting the sensor to the intensity meter, we observed different intensities of laser for different PDI plates at the intensity meter. We took two sets of measurements by setting the initial intensity of the laser through the power regulator.

5.1.2 Equations for absorption coefficient of NiCr.

Here, we calculate the absorption coefficient of NiCr by taking two sets of readings. We have taken into consideration all the reflected intensities, transmitted intensities and power losses due to absorption coefficient of NiCr and Glass. The calculation of absorption coefficient () and transmittance is done as follows.

Figure : Factors contributing to the transmittance of light through semi-transparent plate

From Figure 14, we can properly understand the whole process through which the light transmits through a semi-transparent plate. When incident light (I0) strikes the NiCr surface, a part of it is reflected back which is denoted as IR1 and part of it is transmitted through NiCr with some losses due to its absorption coefficient α1. It is denoted as I1, and it is given as;

When this I­1 strikes on the interface of NiCr and glass some of it is reflected back i.e. IR2. The part of it transmitted through the NiCr substrate, with some losses due to absorption coefficient α1, is known as "I2". It is given as

When this I2 comes out of glass and enters air, part of it is reflected back, denoted as IR3; the other part is absorbed in the glass (α2) transmitted out as Ix, which is given as,

We approximated the absorption coefficient of glass (α2) to zero as ideally there is no absorption loss in glass.

All the constants in the above equation are taken as a single constant, B, given as,

So,

5.1.3 Measurements

The measurements are taken by using the setup described in section 5.1.1. There is a power regulator in front of HeNe gas laser which is used to control the power of laser light, which strikes the semi-transparent plate. The following two tables are prepared by measuring the output laser intensity which is passed through the semi-transparent plate. In first set of measurements the initial intensity (I0) is taken as 1002μW and in the second set, the initial intensity is taken as 2003μW.

Thickness of NiCr,

nm

Power(without Plate), I0, μW

Power(With Plate),

Ix, μW

Transmittance

(ratio)

0

1002

951

0.9491

7.5

1003

358

0.3569

34

1003

73.9

0.073

42

1003

29.58

0.0295

60

1003

10.16

0.01012

Thickness of NiCr,

nm

Power(without Plate), I0, μW

Power(With Plate),

Ix, μW

Transmittance

(ratio)

0

2001

1850

0.9245

7.5

2003

717

0.3579

34

2004

157.1

0.078

42

2003

58.4

0.0294

60

2003

21.46

0.01071

The following two graphs are obtained by plotting the values of thickness against the transmittances from the tables above. These graphs are first plotted and then fitted to the exponential expression:

As it is shown that the above two graphs have very similar values, to get a mean or average value of both graphs, both sets of measurements have to be plotted in the same graph. To obtain a combined graph, the previous two sets of measurements are combined in the following table.

Thickness of NiCr,

nm

Power(without Plate), I0, μW

Power(With Plate),

Ix, μW

Transmittance

(ratio)

7.5

1003

358

0.3569

34

1003

73.9

0.073

42

1003

29.58

0.0295

60

1003

10.16

0.01012

7.5

2003

717

0.3579

34

2004

157.1

0.078

42

2003

58.4

0.0294

60

2003

21.46

0.01071

This graph is obtained by merging the values of table 1 and table 2 to get an average value of the exponential fit.

5.1.4 Calculations

When the values in the merged graph are fitted exponentially, we get an exponential equation describing the pattern in the values. This equations is as follows

y = 0.6237e-0.068x

By comparing it with the equation

We can get α= 0.068 m-1

And B=0.6237

By using these values of B and α, we can estimate the thickness of NiCr to be coated for 2% and 4% transmittance.

For 2%:

By putting the values of α and B in the above equation, we will get the value of thickness of NiCr as

x=50.58 nm

For 4%:

By putting the values of α and B in above equation, we will get the value of thickness of NiCr as

x=40.39 nm

These are the required thicknesses of the semitransparent plates to be prepared.

5.2 Testing for relationship between reflectivity and thickness of NiCr.

In this section, we are going to establish a relationship between thickness of NiCr and the reflection of light through semitransparent point diffraction interferometer plates. An experimental setup is described below to find the relationship.

5.2.1 Experimental setup

To find the reflection we passed the light through a power regulator .The light passed from the regulator and was allowed to hit the surface of the PDI plate. After reflection, the beam of light goes to Thorlabs light intensity sensor. By using the intensity meter we observe the different reflected intensities of light for different plates. Three sets of readings were obtained in this exercise.

5.2.2 Measurements

The measurements are taken by using the setup described above. There is a power regulator in front of the HeNe Gas laser which is used to control the power of laser light which strikes the semi-transparent plate. The following three tables are prepared by taking the measurement of output laser intensity which is reflected against the semi-transparent plate. In first set of measurements the initial intensity (I0) is set at 2mW and in the second set the initial intensity is taken as 1.454mW and, in the third set of measurements, the initial intensity is 1.567mW.

The measurements are shown in tabular form in the following tables.

Thickness of Plate

(nm)

Initial Intensity, I0

(mW)

Reflected Intensity, IR

(mW)

Mirror

2

2

1

7.5

2

.279

0.1395

34

2

.776

0.388

42

2

.819

0.4095

60

2

.759

0.3795

Thickness of Plate

(nm)

Initial Intensity, I0

(mW)

Reflected Intensity, IR

(mW)

Mirror

1.454

1.454

1

7.5nm

1.454

.2218

0.1525

34

1.454

.601

0.4133

42

1.454

.636

0.4368

60

1.454

.591

0.406

Thickness of Plate

(nm)

Initial Intensity, I0

(mW)

Reflected Intensity, IR

(mW)

Mirror

1.567

1.567

1

7.5nm

1.567

0.223

0.1423

34

1.567

0.616

0.393

42

1.567

0.649

0.414

60

1.567

0.604

0.385

5.2.3 Calculations for reflection of light from tables

To calculate the reflection of light, we used the tables above. From all the three tables the values of the ratio between initial and reflected intensities for the mirror and 7.5nm plate are not considered as the mirror has almost 100% reflectance, and the transmittance for 7.5nm plate is very high.

We know that

Since,

So,

Here,

So,

We can calculate the value of "R" by taking the mean values of 34nm, 42nm and 60nm respectively. So by taking the mean values from three mentioned tables we have,

n=9 and X=0.385, 0.414, 0.393, 0.406, 0.4368, 0.4133, 0.3795, 0.4095, 0.388

The mean value of the above data thus becomes:

This is the required value of "R".

The value of "C" can be calculated by using above expression we derived,

C=1-R

C=1-0.40279

C=0.59271

Similarly, we can calculate the Standard deviation by using the following formula;

We get

SD (σ) =0.0181

5.3 Results and discussion

From the measurements in the last two experiments, it becomes clear that the transmittance of light is decreasing as the thickness of NiCr is increasing.

From our calculations in first experiment, we got the value for constant (B) of 0.6237 and a value of Absorption coefficient (α) of 0.068m-1. From these values, we can suggest that, for 2% and 4% transmittance, the thickness of NiCr should be 50.587nm and 40.394nm. From the calculations in the second experiment, we got the value of C as 0.59271.

If we look at the expression of transmittance from first experiment, which is:

To find the ideal transmission we can assume absorption coefficient for NiCr equals zero, which gives us the ideal transmission from the first experiment as follows

From second experiment we have,

Let us assume, for ideal transmission, loss due to absorption (A) is zero then,

If we compare transmission from the first experiment (T1) and transmittance from the second experiment (T2), we can comfortably say that both are nearly equal within the error range which is calculated as ±0.0181 (standard deviation). This result shows the consistency of our data.

We have forwarded our requirements to the MC2 lab for the fabrication of the PDI plates according to our design and specifications.

6 Conclusion

Our main goal, to design and develop new PDI plates for the existing PDI system, is achieved, as it was previously discussed that the old PDI plate is broken and unable to give us accurate readings.

The complete designing and developing process was discussed in detail. The first step was to test the semi-transparent plates for obtaining the relationship between the transmittance of light and the thickness of the NiCr coating. In this step, we have first measured the transmittance of light through test plates with the thicknesses 7.5nm, 34nm, 42nm and 60nm. These measurements were used to calculate the absorption coefficient α of NiCr, which was found to be 0.068m-1, and the value of the constant B which amounts to 0.6237. In the second experiment, the value of the constant, C, was calculated from reflectivity measurements on the test plates. The value came out to be 0.5927.

In the second step, the design was made according to the results deduced in the first step. There were some basic changes in the physical design from the previous plate made in 1992. These changes assure better performance and more accurate readings. It also assures easier handling and experiment setup. Our design has also ensured easier commercial production of the PDI plates in the future, as the basic 4-inch mask is present with the proper design specification in the graphical format.

These plates will be used in the project for measuring surface roughness for mechanical engineering applications in the near future.

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