Autocollimator Operation Principle

Published Date: 02 Nov 2017

Introduction

General introduction:

The optical systems represent a system that deals with the light in a desirable way to form a real or a virtual image, in order to create an optical spectrum, or producing a light that has a specified wave length or polarization. In addition, instrumentation is the science of control and measurement of physical quantities such as distance, angle, flow, temperature level or pressure. Moreover, instrumentation could be done by using several methods such mechanical instruments and optical instruments. The optical instrument is the process of light waves to either enhance an image for viewing or to determine one of number of characteristic properties by analyzing the light waves.

Image enchantments, the telescope was the first optical instruments in this class, which as about magnifying distant imaging, followed by the microscope which used for magnification of very tiny images. However, the image enchantments by using optical instruments was improved, since the days of Van Leeuwenhoek and Galileo.

Light wave analysis, the light wave analysis was used in several applications such the photometer which its objective is to measure the light intensity, Polari-meter which used to measure the rotation and dispersion of polarized light, Reflecto-meter for measuring the reflectivity of a surface, Refracto-meter which used to measure the refractive index of a material, Autocollimator for measuring the angular deflection, and many other applications.

In addition, the optical instruments has the advantage of being very sensitive, which means a small change in the light wave will leads to have a different results. Another advantage is that the optical instruments are easy to build. Furthermore, the optical instruments are cheap comparing to the other instruments methods, in addition, of being safe to use for both the user and the object since there will be no direct contact which might harm sensitive objects.

Objective:

The aim of this project is to design an analogue electronic system to convert the generated signal from the autocollimator to an electrical signal that is ready to be displayed in order to measure an angle of 1 arcsec.

Background information:

Autocollimator:

Measuring the straightness, flatness, and squareness of work components is required in many industries. Since most of these industries required a measurement with an angel that is below 5 µrad, which represents a considerable challenge to the metrology instruments employed. In addition, optical Autocollimator is an optical instruments that being used to measure the flatness, the straightness of an objects by measuring the small angle change. The optical collimator consists of mechanical components, optical components and electronic system as long as the software. The optical Autocollimator, has the advantage of being very sensitive, cheap and easy to build comparing to the other surface profilers. In addition, of being safe since no direct contact between the autocollimator and the surface, while the mechanical profiler will have a direct contact with the surface which might damage. However, the autocollimator could be either be visual or electronic figure (). The electronic autocollimator will provide more accurate results.

2.1.1 Autocollimator operation principle:

Both the visual and the electronic autocollimator has the same basic principle which is, any surface undulation of the latter will change the direction of the light beam reflected off its surface. In addition, the difference between the visual and the electronic autocollimator is that, the angular deviation of the light beam will be measured by using an eyepiece, while in the electronic autocollimator the reflected light will be measured by using a position sensing detector(PSD).

In terms of the electronic autocollimator, as shown above in figure (), when the laser beam hit a surface which has an angle of (α) than the beam will be reflected from the surface into the position sensing detector ( PSD) with an angle of (2 α). As a result, the change in the light position at the PSD will be, where is (f) is the focal length.

Position sensing detector (PSD):

The position sensing detector (PSD), is an opto-electronic device that produce and continuous position data from an incident light spot. Using the PSD has advantages of having a fast response, excellent linearity and high resolution. In addition, there several types of PSD such as 1- dimensional PSD which used to measure the thickness, height and angles. 2-dimensional PSD which is used to measure the straightness and flatness. Figure () shows the 1- dimensional PSD.

As shown above in figure (), when the incident light hits the PSD surface, two output continuous current will be produced Y1 and Y2, where the relationship between the light position and the current is driven by :

In addition, when the surface angle is 0 degree the incident light will hits the PSD at the middle (position A). However, by changing the surface angle by 1arcsec the incident light will have a (position B). As a result, in order to measure the 1arcsec angle that means the system noise must be less than the difference in the current between the two positions.

Noise:

Noise is a fundamental parameter to be considered in an electronic design as it typically limits the overall performance of the system. However, all electronic systems suffer from several noise sources either external or internal. The external noise refers to the noise that generated from an outside source such as the noise generated by applying a signal to the circuit. On the other hand, the internal noise refers to the generated noise from the electronic components such as resistors. In addition, the internal noise could be generated from various reasons, however, some types of the internal noise has a very low value which could be ignored during the calculating while other needs to be minimized as much as possible such as thermal noise, flicker noise and shot noise. In addition, the overall system noise could be calculated by:

Thermal noise:

The thermal noise is also called Johnson noise or Nyquist noise. This types of noise occur in all electronic components. The thermal noise is generated from the thermal motion of charged particles in a resistive element. However, the thermal noise depends on three variables which are temperature, resistance and bandwidth, since the thermal noise does not depend on the frequency than it is a type of white noise.

Where: k is Boltzmann's constant.

Shot noise:

Shot noise is a type of electronic noise which originates from the discrete nature of the electric charge. In addition, the shot noise depends on both the bandwidth and the current, since the shot noise independent on the frequency than it is a white noise. Shot noise could be calculated by using this formula:

Flicker noise:

The flicker noise is also called 1/f noise. The flicker noise is refers to the phenomenal of spectral density which occur in all frequency components. In addition, the flicker noise depends on frequency and the component characteristic. However, since the flicker noise depends on the frequency then it is a pink noise. However, the flicker noise is inversely proportional to the frequency.

Methodology

When the reflected laser beam from the surface hits the position sensing detector two output current will be generated Y1 and Y2. In addition, these generated currents depends on the signal power, PSD sensitivity, the PSD length as well as the incident light position on the PSD. Since, the PSD sensitivity and length are constant the two changing variables will be the signal power and the incident light position. However, having the measurements depending on the signal power will provides errors, since during the experiments the signal power might change. In order to solve this problem the position formula that does not depends on the signal power was derived.

Where:

(Hint: the reason for choosing these values will be explained later in chapter 4).

So:-𝟏= 𝑦s on the signal power was drived and the incident light position he calculating while other needs to be mani

In addition, the position Î"Y should be the output from the electronic system. As result, the electronic system will contain of three different circuits, which are the differential amplifier which will produce (Y2-Y1) and a summing amplifier which will produce (Y2+Y1) and the out of these two amplifier will inter a third circuit which will produce (. In addition, the laser beam is a DC source in order to convert it into an AC signal a laser beam chopper was used figure(), the reason for converting the laser DC signal into an AC signal is to be able to minimize the amount of noise in the system.

However, the electronic system will needs more than these three circuits to work and produce an acceptable results. Since, the output current from the (PSD) is very low. A current to voltage convertor circuit (Tranimpedance amplifier) was used in order to convert the low level current into a usable voltage. Furthermore, in order to minimize the amount of noise in the system the Tranimpedance amplifier was followed by an analogue filter. After that, a rectifier circuit was used to convert the AC signal from the filter into DC signal that is ready to be analyzed. However, since the PSD. As result, figure () shows the block diagram for the electronic system.

In terms of meeting the requirement, In order to build an electronic system that is able to measure a surface that has an angle of 1 arcsec the total amount of noise in the system must not exceed the different in the two current at the middle and at 1arcsec. For that the difference in the currents must be calculated before starting the design. This calculation was done only for Y1 since Y2 is exactly the same.

Y1 at the middle (Î"Y=0), since (

Y1 at the at (

The maximum amount of noise should not exceed the difference between the current at the two positions which means:

Circuit design and implementation:

Transimpedance amplifier (TIA) design:

This section is about designing an electronic circuit to convert the low level current that has been generated from the photo detector into usable voltage, figure () shows the standard Tranimpedance circuit while using an ideal amplifier:

Where:

Is: signal current. If: feedback current.

Rf: feedback resistor. Ineg: negative input bias current.

Vout: output voltage.

The Tranimpedance amplifier gain:

By using Kirchhoff law at node A:

Ideal amplifier (Ineg=0)

So, all the current flow through the feedback resistor Rf :

Ideal amplifier (Vneg=0)

:

There are four considerations that need to be taken into account while designing a real Tranimpedance amplifier circuit and these considerations are choosing the photodiode, choosing the amplifier, measuring the feedback resistor value and stabilizing the circuit.

Photodiode:

Figure () shows the photodiode equivalent circuit.

Photodiode current (Iph):

Which represents the current that generated from the photodiode action.

Junction capacitance (Cj):

Which represents the capacitance that occurs from the depletion region of the diode. However, the lower the junction capacitance the wider the depletion region which leads to a faster response. So the response speed is inversely proportional to the junction capacitance.

Shunt resistance (Rsh):

Which represents the impedance of the current source. However, Ideal photodiode has an infinite shunt resistance.

Series resistance (Rs):

Which represents the resistance of the semiconductor material which usually has a value that less than 100Ω which can generally be ignored.

In addition, the photodiode could be either connected in photoconductive mode or photovoltaic mode. The difference between the photoconductive mode and photovoltaic mode is that the photoconductive mode, an external reversed bias voltage is applied, which increase the width of the depletion region and reduce the junction capacitance. The advantage of the photoconductive mode is that the response speed will increase since the junction capacitance is reduced. However, the disadvantage is that the reversed bias voltage will flow through the shunt resistance and produce a leakage current that called dark current. The dark current is directly proportional to the applied voltage as well as the temperature, while usually the dark current is doubled for every 10 °C. In addition, the dark current will be converted into voltage by the transcendence amplifier and appear as a noise in the output. On the other hand, the photovoltaic mode has a lower response speed than the photoconductive mode but no dark current so has a less noise than the photoconductive mode.

In terms of choosing the photodiode, the photodiode that was used during the project is S3931 from Hamamatsu. Figure () shows the relationship between the light wavelength and the sensitivity.

Since the laser that was used during the project has a red color that means the laser wavelength is 620 nm. From figure () the photosensitivity for the photodiode S3931 at 620nm is equal 0.4A/W. In addition, the photodiode has a low value of junction capacitance which equal 40pF. Since the value of the junction capacitance is low the Tranimpedance amplifier circuit was connected in photovoltaic mode.

Amplifier:

The Tranimpedance amplifier convert the input current into a usable voltage value. Although the signal strength is relatively large, the change in the signal level due to the change in the measurement is extremely small. So while choosing the amplifier some considerations needs to be taken into account.

The amplifier must have a small value of input bias current, since the input bias current will be convert into voltage by passing through the feedback resistor and will appear in the output as voltage noise.

The amplifier must have low input offset voltage, otherwise the output will be 0V at non-zero input.

The amplifier must have a small value of input flicker noise, to minimize the overall noise.

Voltage feedback amplifier is best choice to meet the above requirements. In addition, the amplifier that was used during the project is OPA657 from Texas Instruments. The reasons for choosing OPA657 are that, it has a very low bias current (2pA) which could be ignored, low offset voltage (0.25mV) and a low flicker noise. Figure () shows the amplifier flicker noise.

Feedback Resistor:

Since the amplifier that being used in this project is OPA657 which has very small bias current (2pA) which could be ignored.

The maximum input current from the photodiode (Imax):

Where:

Light beam power: P=0.1mW

Sensitivity:

By using Kirchhoff law

So, All the current flow through the feedback resistor Rf :

Since the amplifier supply voltage is ±5V, taking 80% of this value as the maximum value in order to be in safe side:

Since the Tranimpedance amplifier gain is equal to the value of the feedback resistor that leads to have

Stabilizing the circuit:

The op-amp circuit has a noise gain that equal 1/f. In addition, the transimpedance amplifier circuit is a differentiator circuit which means that the total input capacitance (Ct) will add a zero in 1/f which leads to have unstable circuit. The transimpedance amplifier circuit could be stabilized by adding a feedback capacitor which will insert a pole.

Where:

Ct: total input capacitance. Cdiff=input differential capacitance

Cj: diode junction capacitance. Ccom=input common mode capacitance

Cin: amplifier input capacitance.

Since OPA657 was used which has a 0.7pF differential capacitance and 4.5pF common mode capacitance as it shown in figure () below:

There are two different frequencies need to be take into consideration which are , the zero frequency fz and the pole frequency fp. The zero frequency (fz) depends on the total input capacitance (Ct) and the parallel combination of the feedback resistor and the shunt resistance. While the pole frequency is depends on the feedback resistor and capacitor.

Zero frequency:

Since:

Pole frequency:

However, figure () shows three different situations while calculating the value of the feedback capacitor:

The feedback capacitor value is too small:

If the feedback capacitor is too small that will leads to have the pole frequency to fall outside the open loop gain for the amplifier. As result the system will be unstable. Pole frequency fp1 in figure ().

The feedback capacitor value is too large:

If the feedback capacitor is too large that will leads to have the pole frequency to fall inside the open loop gain for the amplifier. As result the system will be unconditionally stable but has a slow response: Pole frequency fp2 in figure (). In addition, if Cf= Ct that will leads to have flat noise gain which is very stable but has a very slow response).

The feedback capacitor value is optimum:

If the feedback capacitor is optimum that will leads to have the pole frequency to fall on the open loop gain for the amplifier. As result the system will be stable while having a good response speed. Pole frequency fp3 in figure (). The optimum feedback capacitor good be determined by:

Closed loop gain:

Which must be equal to the open loop gain at the pole frequency:

By letting both gain equal:

Since:

GBW= gain bandwidth product =1.6GHz.

Rf=feedback resistor =100kΩ.

Ct=total input capacitance =45.2Pf.

Final Transimpedance amplifier circuit:

Transimpedance amplifier circuit bandwidth:

Transimpedance amplifier circuit gain:

Figure () shows the DC sweep analysis by using PSpice software:

Band pass Filter design:

The Transimpedance amplifier convert the low level current that was generated from the photodiode into usable voltage. In addition, the Transimpedance amplifier has a very large bandwidth which is equal to 7.5MHz. However, this large bandwidth will leads to have high amount of shot and thermal noise , since the shot and the thermal noise is directly proportional to the square root of the bandwidth. Moreover, the Transimpedance amplifier will also provide a flicker noise. In order to reduce the amount of shot and thermal noise the signal bandwidth need to be reduced into a reasonable amount, and the signal frequency need to be chosen carefully in order to minimize the amount of flicker noise.

The band pass filter was used in order to reduce the system bandwidth and to eliminate the flicker noise that occur outside the desired signal frequency. There are two considerations need to be taken into account while designing the band pass filter which are, choosing the band pass filter network class, choosing the signal bandwidth frequency.

Network synthesis filter:

Network synthesis method is the opposite of network analysis method. In addition, each network consist of three parts which are network elements, input (excitation) and output (response from network). For network analysis method, the network elements and the excitation are already known while the output response is optioned after analyzing the network. However, for the network synthesis method the excitation is known and the desired response was selected while network elements was calculated in order to satisfy the requirements.

The network synthesis method produced different classes which includes Butterworth, Chebyshev and Elliptic. The filter class describe the class of the mathematical polynomial. The Butterworth filter has the flattest pass band. However, the Chebyshev filter allows ripples in order to achieve faster cut-off transition. In addition, Chebyshev filter had two different types. Type one allows the ripples in the pass band, while type two allows the ripples in the stop band. The Elliptic filter has even faster cut-off transition but at the expenses of having ripples in both the pass band and the stop band. Figure ( ) shows the low pass frequency response for three different classes.

In terms of choosing the best filter class for this project, since the input is just a single signal that means having a ripple in the pass band will not affect the signal, while having a ripples in the stop band will leads to have more noise. As a result, the Chebyshev type one is the best choice for this project, since it has a faster cut-off than the Butterworth filter and the allowed ripples occur in the pass band rather than the stop band (Chebyshev type two filter and Elliptic filter). In addition, increasing the pass band ripple value will leads to have a faster cur-off transition which means less noise. Moreover, increasing the filter order will leads to allow more ripples in the pass band so a faster cut-off transition which also means a less noise. As a result, the filter specifications that was used is (band pass filter fourth order, 3dB ripple, 2 kHz central frequency (f0) and 100 bandwidth), the reasons for choosing these values will be explained later on.

Chebyshev filter transfer function:

The band pass filter transfer function calculation was divided into two parts. Part one, the calculation for the normalized Chebyshev second order low pass filter, while Part two is about un-normalizing the transfer function for the Chebyshev second order low pass filter into a Chebyshev fourth order band pass filter.

Normalized transfer function :

In order to calculate the Chebyshev transfer function the pole location need to be calculated first. The pole location is defined by two different variables which are (D) and (Ï•) where:

Where:

The normalized filter order: n =2. Allowed pass band ripple: apass = -3dB

m=0, 1, 2……… : m=0.

The pole location could now be described as a complex number where the real part is () and the imaginary part is ( where:

So:

The Chebyshev normalized transfer function is in the form of:

Where:

, ,

So:

, ,

The second order Chebyshev normalized transfer function:

Un-normalized transfer function:

In order to un-normalize the low pass transfer function into a band pass transfer function the variable (S) need to be changed into (Sp) where :

Angular frequency:

Bandwidth in rad:

So:

Replacing (S) by (Sp):

As a result, the transfer function for the fourth order band pass Chebyshev with central frequency 2 kHz and 100 Hz bandwidth is

Where:

The quality factor (Q) is equal:

Flicker noise calculation :

The fourth order polynomial equation for the OPA657 amplifier flicker noise was generated by using MATLAB :( Appendix 1)

After generating the flicker noise polynomial equation, it is possible to calculate the amount of the flicker noise that is allowed to pass through the band pass filter and this is done by integrating the multiplication of the flicker noise equation with the band pass filter transfer function.

Flicker noise passing through the band pass filter Nf(bp):

For 2 kHz central frequency and 100Hz bandwidth,

The integration was calculated by using MATLAB (Appendix 2), In addition, since the output signal from the Transimpedance amplifier circuit is single signal that means that bandwidth should be equal 0 Hz. On the other hand, in reality the signal might not occur in the exact center frequency during to vibration that might occur during the experiment for that a 100Hz bandwidth was chosen in order to solve this problem. However, the transfer function coefficients and calculation of the flicker noise was done several time by MATLAB, in order to choose the best frequency. Since, the transfer function nominator depends on the bandwidth not the central frequency that means by making the bandwidth constant (100Hz) the transfer function nominator will be constant ( even by changing the central frequency. Table () shows the results of the quality factor, transfer function dominator and the flicker noise at different frequencies.

F0 (kHz)

Q

Transfer function (dominator)

Flicker noise (nV)

1

10

1.566

2

20

0.740

3

30

0.487

4

40

0.365

5

50

0.293

6

60

0.245

As shown above in table (), the flicker noise at 1 kHz is 1.566nV. However, the flicker noise was reduced by a factor of two when a 2 kHz frequency was used. In addition, at 2 kHz the flicker noise is equal 0.74nV which is far lower than the amount of the minimum total noise in order to measure an angle of ,1 arcsec. Since increasing the frequency of the system more than 2 kHz will only reduce the flicker noise with a small amount and since the signal frequency will be generated by a mechanical device the system central frequency was chosen to be at 2 kHz.

Band pass filter circuit implementation :

In terms of implementing the band pass circuit, there are two most common circuit configurations, Sallen key topology (voltage-controlled voltage source) and multiple feedback topology. Choosing the circuit topology depends on the system requirements. The Sallen key topology figure () has the advantage of having more accurate gain than the multiple feedback topology. Since, the Sallen key topology gain depends on two external resistors value, while the multiple feedback topology gain depends the input and the feedback resisters ratio. However, the multiple feedback topology figure () had a better high frequency behavior and a better sensitivity to the components variation. Moreover, in order to keep a unity gain and since the system will be applied at low frequency the Sallen key topology was selected to build the band pass filter.

Sallen key topology components calculation:

The Sallen key topology use one op-amp to deal with two pole-section. As a result, a fourth order band pass filter will have two stages. In addition, the components was calculated by using Filter pro softwere:

Figure () shows AC sweep analysis by using PSpice software by assuming the input voltage is (1V).

AC to DC convertor:

The output signal from the band pass filter is an AC signal, which means its need to be converted into DC before analyzing it. Converting the AC signal into a DC signal could be done by using a rectifier circuit. In addition, the rectifier circuit could either be a half wave rectifier which passes the positive signal while reject the negative signal , or a full wave rectifier which will allows the positive signal to pass and converting the negative signal into positive as shown in figure (). Moreover, the full wave rectifier will produce steadier DC signal than the half wave rectifier, since the output voltage will has a lower ripple value.

The full wave rectifier circuit could be active circuit or non-active circuit. In addition, the non-active rectifier has the advantage of using less components than the active rectifier so it is going to be cheaper. However, the non-active rectifier circuit uses four diodes two of them are forward bias, while the other two are in reversed bias. Since, the positive cycle and the negative cycle depends on two diode, that will leads to have a voltage drop that equal to two diodes voltage drop, since generally the voltage drop per diode is 0.7V, than both the positive and the negative cycles will have a voltage drop that equal 1.4V which will leads to have and output voltage will be less than the input voltage by 1.4V. However, in this project the input voltage might have any value between 0V and 4V, as a result having a 1.4V drop is not acceptable. Another advantage that the active rectifier has over the non-active rectifier is that the active rectifier gain could be changed. In order to build a rectifier circuit that has lower voltage drop an active rectifier circuit was used. In addition to design an active full wave rectifier a half wave rectifier needs to be designed.

Half wave active rectifier:

Figure () shows the half wave active rectifier circuit. The circuit analysis was divided into two sections which are the negative cycle and the positive cycle. Firstly, during the negative cycle the diode (D1) will be active, as a result during the negative cycle there will be an output voltage. Secondly, during the positive cycle the diode (D1) will be in active (reversed) so the output voltage during the positive cycle should saturate at 0V. However, during the positive cycle the Op-amp will saturate at a negative op-amp supply voltage (usually -15V), which will leads to have a large time delay. In order to solve this problem another diode was added figure (). This new diode will insure that the output will saturate at the negative diode voltage drop (usually -0.7V) instead of having the saturation at negative Op-amp supply voltage. As result the time delay will be reduced dramatically. In addition, the new diode (D2) is called catching diode since its catch the output from going to (-15V) and clamps it to (-0.7V). In addition, the rectifier gain is equal to ( ).

Full wave active rectifier:

There are several methods that converts the half wave rectifier into a full wave rectifier, two of these methods will be discussed. The first method is done by using one op-amp while second method is about using two op-amps.

Full wave rectifier using one Op-amp:

This method is about adding one more resistor that passes the input signal to the output. Figure () shows the configuration of the circuit. However, the positive cycle gain is equal to () while the negative cycle gain is equal to , so in order to have the same value for both gain and. So the gain for both cycles will become () =0.5. However, since the input voltage is low, using this circuit will not give the best result. However, by assuming the input voltage is 2V, R2=R3=10kΩ and R1=20kΩ. The circuit was simulated by using PSpice software and the result was shown in figure ().In addition, the full wave active rectifier using one Op-amp is better than the passive rectifier because it has one diode that actually doing the rectification, so the voltage drop in the active rectifier will be half that in the passive rectifier. However, the disadvantage is that this configuration has a gain of 0.5.

Full wave rectifier using two Op-amps:

The active rectifier using two op-amps is preferable in this project because it has low voltage drop and a gain that is larger than 1. Figure () shows the circuit configuration for this type. In order to explain this circuit, the circuit was divided into two stages, where the first stage is the rectification section while the second stage is the amplification section. Since the stage 2 is an inverting amplifier the diodes in stage one was rotated in order to let the positive cycle to pass while blocking the negative cycle.

There are two outputs from stage 1, at point (A) the system allows the positive cycle to pass since the current will flow through Diode 1 (forward bias), while blocking the negative cycle since the current will not be able to pass through Diode 1 (reversed bias). However, the signal at point (B) will be the same as the input signal. Figure () shows the signal at (input, point A, point B) respectively by assuming the input voltage is (2V). In addition, these two signals have the same amplitude then adding them together without an amplification will leads to have only the negative cycle since the positive cycle will be canceled. So, in order to have an output signal that include both the positive and the negative cycle, the gain of the signal sot the negative input point (A) should be double the gain at positive input point (B) this is why the second stage was used.

So after including the second stage the gain for both the positive and the negative cycle could be calculated by:

For this project a system of a minimum gain that equal (2) is required, since a low input voltage might occur for that the resistors value that was used are:

R1=R2=R4=10kΩ , R3=5kΩ, R5=20kΩ

So,

So the overall gain is (2), Figure (), shows the input signal and the system output signal:

The next step is to add a smoothing circuit (Low pass filter) in order to produce a steady DC voltage. However, the output DC voltage could be calculated by using:

In addition, increasing the time constant will leads to have a lower output ripples in the expense that the amplifier will take more time to reach the study state. So by choosing the capacitor to be equal 100nF, and the resistor to be 100kΩ. Figure () showing the final circuit diagram while figure () shows the system output

Summing amplifier:

Difference amplifier

Conclusion: