15002

Examensarbete 15 hpJuni 2015

Investigation of Improvement of Pellet Tracking System

Sanne TorgersenAdéle Wallin

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

Investigation of Improvement of Pellet TrackingSystem

Sanne Torgersen, Adéle Wallin

A pellet target is an internal target system for accelerator experiments in nuclear and particle physics. The target consist of small spheres of frozen hydrogen, called pellets. The pellets interact with high energy accelerator-beam particles in a particle accelerator. The challenge is to track these pellets for good accuracy of interaction position in both time and space. The pellets are tracked with lasers and cameras. The main goal of this project was to develop a method to find the best time resolution and to optimize the efficiency of the pellet tracking system. This project addresses challenges with making trustworthy measurements were stability in the setup, difficulties with alignment and optimizing of exposure cycles. Because of stability issues, a more stable and robust module that also will ease adjustment of alignment is under construction. A well-aligned setup can be confirmed in two ways. Firstly by confirming that the cameras detect pellet signals for a about 300 micron-height change of the laseror the camera and secondly that a focus interval is within 100 micron. A mathematical model that calculates class-distributions for varying exposure cycles and shifts can be used to predict the results from a measurement with pellets. The model can be used for testing an appropriate exposure cycle before running it with pellets. In addition, an appropriate laser power should be chosen since the effects of both too low or too high power gives misleading results. This project has contributed to progress in the field of pellet tracking.

ISSN: 1401-5757, 15002Examinator: Tord JohanssonÄmnesgranskare: Martin SjödinHandledare: Hans Calén

Contents

1 Populärvetenskaplig sammanfattning 2

2 Introduction 32.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Problem and task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.4 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.4.1 The setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.4.2 Exposure cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.4.3 Pulse length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.4.4 Focus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.4.5 Laser power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.4.6 Multiple �shing lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 Results 63.1 Exposure cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.2 Pulse length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.3 Focus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.4 Laser power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.5 Multiple �shing lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4 Discussion 124.1 Exposure cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.2 Pulse length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.3 Focus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.4 Laser power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.5 Measurements with two �shing lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5 Conclusion 13

6 References 14

1

1 Populärvetenskaplig sammanfattning

I det här projektet har vi haft som målsättning att optimera tidsupplösningen och e�ektiviteten i ett spårningssys-tem för vätepellets. Vätepellets är mycket små sfärer av fryst väte, som skickas genom en stråle av laddade partiklarsom accelererats till höga energier i en partikelaccelerator. När strålen av vätepellets passerar acceleratorstrålen kankollisioner och därmed reaktioner ske. Då är det viktigt att veta den exakta positionen för pelleten där reaktionenhände. Pelletarna spåras med hjälp av lasrar och kameror som sitter i olika plan för att mäta, bland annat, posi-tion och hastighet. Detta spårningssystem behövde optimeras på �era olika sätt, inga systematiska eller utförligamätningar hade tidigare genomförts för att undersöka varför olika resultat inte stämde helt med teoretiska förvänt-ningar. Efter mätningar vid en testbänksuppställning och analys av hur tidsskift, exponeringstid, höjdposition avlaserstrålen och mycket annat påverkar resultatet �nns nu ett sätt att förutsäga vilka resultat körningar med pelletskommer att ge. Det �nns även ett sätt att kontrollera att kamerorna och lasrarna är upplinjerade.

2

2 Introduction

2.1 Background

This project is about an optical tracking system for pellet targets. A pellet target generator is an internal targetsystem for accelerator experiments in nuclear and particle physics. The target system consists of a generator wherea jet of liquid hydrogen is broken up into droplets with a diameter of about 20 − 35µm by a nozzle vibrating ata �xed frequency in the range of 40 − 100 kHz. The pellets freeze by evaporation in a droplet chamber and forma beam of pellets that are injected in vacuum via a 7 cm long capillary. After collimation, the pellets are directedthrough a thin pipe (φ ∼ 5mm) of several meters through the detector system of the experiment into the scatteringchamber and further down to a pellet beam dump. In the scattering chamber they interact with a high energyaccelerator beam of e.g. protons, anti-protons or deuterons.[1],[2] The technique is used in experiments in Germanyand is planned to be used in the antiproton storage ring HESR. An optical tracking system for the pellets that wouldallow a precise three dimensional determination of the interaction-point between the pellet and an accelerator-beamparticle is being developed within this project at IFA1 and TSL2 in Uppsala.

2.2 Problem and task

To achieve a precise three dimensional determination of the interaction point between a pellet and an acceleratorbeam particle the pellet tracking system requires a high resolution in both time and space. With the presentlyavailable line-scan (LS) cameras the repetition frequency of the exposure cycles is around 100 kHz which is almostenough to reach the desired resolution. There is also a dead time of about 3µs between the exposures.

The main goal of this project was to develop a method to improve the time resolution of the pellet trackingsystem and to increase the e�ciency by making the same observation with two cameras with shifted exposures.

2.3 Theory

The pellet tracking system uses LS-cameras with a sub-millimeter thin line of pixels to measure position of individualpellets at a certain time. At one level the pellets are illuminated by two lasers from di�erent directions and there�ected light is detected by two cameras opposite each other. A set of cameras at di�erent levels can be used toreconstruct direction and velocity of the pellets. This requires that the cameras are well aligned and work in asynchronized way so that time di�erences can be measured e�ciently and precisely.

The read-out system is based on commercial frame-grabbers and external synchronization. In the read-outsystem each picture corresponds to one line. One line corresponds therefore to the time of one exposure cycle. Theintensity of any pellet signal is analyzed as a light integral. This is the sum of the amplitudes of all the signalsrecognized as coming from one pellet.

2.4 Method

2.4.1 The setup

The alignment of the equipment was investigated at the Uppsala Pellet Test Station for both pellet runs and with abench test setup based on a pulsed LED/laser illuminating a �shing line, see �gure 1. In the pellet tracking systemthere were two cameras opposite each other, two lasers with a continuous light and a pellet beam with di�usion inboth position and speed. In the bench test setup a known pulse simulated the pellets. The setup using a LED wasmainly used to develop an understanding and skill for handling the equipment. Later the LED was replaced by apulsed laser with a suitable intensity and a more narrow beam of light.

The bench test setup was used study the read-out performance with respect to pulse length, focus of camerasand laser, laser power and electronic e�ects. Moreover the read-out performance was studied with di�erent exposurecycles and shifts for both pellet runs and with the bench test setup, see �gure 2.

1(Institutionen för Fysik och Astronomi) Department of Physics and Astronomy at Uppsala University2The Svedberg Laboratory

3

Figure 1: The bench test setup with two LS-cameras, a LED and a �shing line.

Figure 2: Visualization of two synchronized cameras with a time shift.

2.4.2 Exposure cycle

Di�erent exposure cycles were investigated with di�erent cycle time, exposure time and shift. The read-out systemclassi�es every signal according to when it was seen by the other camera, e.g. when a signal is seen by cameraB in its nth cycle and by camera A in its nth + 1 cycle it's classi�ed as seen by camera B when seen in next lineby camera A and similarly seen by camera A when seen in the previous line by camera B. A mathematical modelbased on the geometric relationship between the exposure cycles and their relative shift was developed to calculatethe distribution for each class. Measurements with varying shift were made at a pellet run for a series di�erentexposure cycles. The cycles that were used were exposure cycles of 20µs with exposure time of 15µs and 10µsand exposure cycles of 13µs with exposure time of 8.5µs, 7µs and 5.5µs. The model was then adjusted to �t themeasured values. Finally the same measurements were made for the bench test setup with the aim to reproducethe pellet data.

2.4.3 Pulse length

Di�erent pulse lengths to the LED/laser input were used to investigate the read-out response to pellets of di�erentsize, speed and e�ects due to overlapping of dead time.

2.4.4 Focus

To investigate the dependence of alignment and focus the position of the laser and the cameras were varied. Firstthe height of the laser was varied through the range in which any signal was observed by the viewing interfaceand the light signals were measured. Then measurements were made where the height of one camera was varied inthe same way. The last measurements were made where the distance between one camera and the �shing line wasvaried through the range in which any signal was observed.

2.4.5 Laser power

The laser power was varied to investigate the read-out response.

2.4.6 Multiple �shing lines

Measurements were made with two �shing lines in the bench test setup. A schematic for the setup is shown in�gure 3. With a known distance between two �shing lines and a known diameter of the two �shing lines it can

4

be calculated how many micrometers corresponds to one pixel. The reason for this test was to investigate opticaland electronic e�ects. Measurements were made with two �shing lines with diameters of 120µm and separationdistance 400µm, 900µm and 1500µm and three amplitudes of the LED input (3V , 5V and 7V ). Additionally,one 120µm-�shing line was replaced with a �shing line with a 200µm diameter and measurement were made forthe same distances and the greatest amplitude (7 V ).

Figure 3: Test setup from above with two �shing lines.

5

3 Results

3.1 Exposure cycle

Measured values from pellet runs with di�erent exposure cycles were plotted against the delay and compared to amodel that calculates the distribution of entries in each class. The model was implemented in MATLAB and thecode is given in appendix A. The model was developed in the following way. It was based on geometric assumptions.After being compared with measured data from pellet runs, the model was adjusted to better �t the data withrespect to assumed electronic e�ects. The model took the pulse length and a minimum time a signal needs to bedetected into account. The minimun time, (min.signal) corresponds to the cut of the light integral. The read-outsystem treats a signal with too small light integral as noise and a longer signal gives a greater light integral than ashorter (with the same amplitude). An example with cycle time of 13µs and an exposure time of 8.5µs is shown in�gure 4. The model was then compared to measurements from the bench test setup and a known pulse length tothe laser input. The values from di�erent exposure cycles with both pellets and the bench test setup were comparedand are shown in �gure 5 and 6. Graphs for some other exposure cycles are found in appendix B.

Figure 4: Measured values from a pellet run with cycle time 13µs and exposure time 8.5µs and corresponding calculated/ap-proximated values for a pulse length of 3µs and a minimun signal time of 0.25µs.

Figure 5: Measured pellet and �shing line run with cycle time of 13µs, exposure time of 7µs and pulse length 2.5µs andcalculated approximation with pulse length 3µs and a minimun signal time of 0.25µs.

6

Figure 6: Measured pellet and �shing line run with cycle time of 13µs, exposure time of 8.5µs and pulse length 2.5µs andcalculated approximation with pulse length 3µs and a minimun signal time of 0.25µs.

3.2 Pulse length

Figure 7 shows the light integral versus the pulse lentgh and increases linearly with increasing pulse length. Whena signal overlaps the dead time it is shown in two following exposure cycles (or lines). When a signal is detected intwo following exposure cycles it is interpreted as two pellets and presented as one line between these pellets. Thenumber of signals shown in two following lines is increasing with increasing pulse length. This is shown in �gure8 where there seems to be a threshold for a pulse length of 1.5µs. The measurements were made for an exposurecycle of 12.5µs with an exposure time of 10µs.

Figure 7: Light integral versus pulse length.

7

Figure 8: Percentage of signals shown in two exposure cycles versus pulse length.

3.3 Focus

The setup was very delicate and dependent of being well-focused and well-aligned. To investigate the read-outresponse dependence of focus, �rst the height of the laser was varied. Figure 9 shows how the camera signalintensity varies with the height of the laser. The width of the horizontal part is about 100µm, which correspondsto the focus interval.

Then the height of camera A and the distance to the �shing line was varied. Figure 10 shows how the intensitydepend on the height of camera A and �gure 11 shows how the intensity depend on a change in distance betweencamera A and the �shing line. In both diagrams camera A detects signals within an interval of 300µm in bothheight and distance when other parameters are optimized. There is also a peak in both diagrams corresponding tothe setting for best focus or alignment. In addition, e�ects of the instability of the setup can also be noted in �gure11. Since the only parameter that was changed was the distance between camera A and the �shing line and theintensity for camera B should therefore barely change we assume the decrease in intensity for camera B is due tosoft bumps to the bench causing camera B to move enough for these e�ects.

Figure 9: Light integral versus laser height.

8

Figure 10: Light integral versus the height of camera A.

Figure 11: Light integral versus the distance of camera A to the �shing line

3.4 Laser power

The e�ect of varying the power of the laser input was that a power less than 3.3mW was too weak and barelygave any signal. A power greater than 4.2mW was too strong and gave an unreadable response. The light integralversus the power of the laser is shown in �gure 12.

Figure 12: Light integral versus laser power.

9

3.5 Multiple �shing lines

The read-out of light signals gives position, signal cluster width and light integral for all entries. In tests with two�shing lines the position occurs like to spikes in the histogram where the position is shown on the x-axis and thenumber of entries is shown on the y-axis. The known separation distance between the �shing lines and the distancebetween the spikes where used to calculate how many micrometers corresponds to one pixel. Then for �shing lineswith a known diameter of 120µm the expected signal cluster width was calculated and compared to the observedwidth.

The test was made for separation distance of 400µm, 900µm and 1500µm and amplitudes of the LED input of3V , 5V and 7V . The measurement with a separation distance of 900µm and the amplitude of the LED input of 7Vis shown in �gure 13. In this case one pixel corresponded to about 30µm, the expected width was 4 pixels and theobserved width was 10 pixels. For the other measurements one pixel seems to correspond to 20− 30µm/pxl. Thisis not consistent resultsa any may be due to non-homogeneous illumination in the �shing lines. In addition, othertests have been done earlier that show that one pixel corresponds to about 35µm. However, for every measurementthe observed signal cluster width is much greater than the expected. It was also found that the interpreted widthincreased with increased amplitude. The measured and expected width for di�erent input-amplitudes are shown in�gure 14. This is partly due to that �leakage� of signal to neighbouring pixels.

When one �shing line was replaced for one with a diameter of 200µm the signal cluster width also exhibitstwo spikes. One spike for each line with di�erent diameter was expected. The result from the measurement withseparation distance 400µm and amplitude of the LED input of 7V is shown in �gure 15. The 200µm-�shing linewas placed closer to the LED. With a 200µm-�shing line mentioned inconsistency is bigger (as expected).

Figure 13: Observed distribution of position and signal cluster width using two �shing lines with a diameter of 120µm, aseparation distance of 900µm and an amplitude of 7V to the LED input.

10

Figure 14: Expected and measured mean of signal cluster width versus distance between �shing lines. Measurements weremade for di�erent amplitudes of the LED input.

Figure 15: Observed distribution of position, signal cluster width and light integral using two �shing lines with diameter of120µm and 200µm, a separation distance of 400µm and an amplitude of 7V to the LED input.

11

4 Discussion

4.1 Exposure cycle

In theory, when the two cameras are perfectly synchronized they should detect the same number of signals and allentries should be seen in the class �same�. Additionally, if e.g. camera B is delayed no signals should be seen inthe class �A in next line� until the delay is greater that the dead time and then increase linearly. This is not thecase though. A reason for this may be that the signal has a signi�cant duration compared to the dead time and ifa su�cient big part of the signal appears in the exposure time it will be measured anyway. Another way to look atthis is as if the dead time is shortened. The dead time is shortened in a way that can be thought of as �on bothsides�, so that some of the signals that are centered in the dead time region partly appear in the same exposurecycle as the reference camera and some of the signals partly appear in the next exposure cycle. Furthermore, asignal needs to appear in the exposure time for a minimum time to be detected at all. The model we developedtakes both this requirement of a minimum time a signal need to be seen, the e�ect of signals centered in the deadtime appearing in the exposure time and a normalization factor into account when calculating the distribution.With a minimum time about 0.25µs the model seemed to �t the pellet-data quite well but not as well for the�shing-line-measurements. The model �t the �shing-line-data much better with a 0.5µs longer pulse as input. It issuspected that due to electronic e�ects a longer pulse is sent out from the pulse-generator in the latter case. Afterthis realization the model was adjusted. The minimum time value of 0.25µs is a value that �t our data but sinceparameter values and cuts for the read-out interface can be changed this is not absolute. One cut is the lower limitof the light integral, all signals below this limit will be treated as noise and cut out from the analysis. In addition,neither the changeover between exposure and dead time nor the square wave is as sharp as the ideal case. Theseelectronic e�ects also a�ect the results.

4.2 Pulse length

The dependence of pulse length was measured to investigate the read-out response to pellets of di�erent size ande�ects due to signals overlapping the dead time. As seen in �gure 7, the light integral increases linearly withincreasing pulse length. Since the light integral is the sum of the amplitude of the signals in all pixels interpretedas one pellet it makes sense that a longer pulse results in a greater integral. Since the pellet beam is illuminatedby a continuous laser beam a longer pulse is analogue to a bigger pellet. In this way it is plausible to calculate thesize of a pellet.

As shown in �gure 8, the percentage of signals shown in two following exposure cycles are shown. In the benchtest setup we use a very low frequency of about 2 kHz corresponding to 40 lines between each signal. The resultimplies therefore that the same signal is shown in two exposure cycles and the only way this is possible is when thesignal overlaps the dead time. Results like this could be used to study electronic e�ects such as how long the deadtime really is when we set it to a controlled value.

Another observation that was made from the pulse length experiment was that camera B had a greater lightintegral in �gure 7. This might be due to non-perfect alignment or if the laser beam was not perfectly orthogonalto the cameras line of view. If the laser was somewhat more directed from the same side of the setup as cameraB a greater amount of light would be re�ected towards camera B than towards camera A and could explain thisdi�erence.

4.3 Focus

From �gure 9 and 10 we see that the focus interval for the camera is about 100µm in height and the signal is visiblein an interval of 300µm. The shape of the curve is symmetric with maximum values on a plateau in the middle.To get the best alignment the camera should therefore be in the middle of the interval where the signals are visible.Since the LS-camera uses pictures of only one pixel in height and one pixel corresponds to about 30µm it seems likethe laser beam is about 250µm wide to be shown for an interval of 300µm, this also makes sense as a comparisonto what we could see with our own eyes (using protection glasses).

In �gure 11 we notice how the light integral for camera B changed even though the distance between camera Aand the �shing line was the only parameter that should have been changed. This is probably due to mechanical

12

instabilities of the setup which is a huge problem. One thing that could be done to overcome this challenge is todevelop a new more sound and robust construction that would be easier to adjust and less sensitive to vibrations.A module just like this is under construction at TSL, Uppsala.

4.4 Laser power

For the �shing-line setup, the most appropriate power of the laser is 4mW . When using a very low power, signalswere not seen at all or cut out as noise. When using higher but still low powers re�ections in the �shing line wasinterpreted as two parallel �shing lines. This was solved by using a higher power. A disadvantage with a too highpower is that the light integral gets unreadable.

4.5 Measurements with two �shing lines

Since we could not �nd out how many micrometers one pixel corresponds to in the measurements, it is possible thatthere is a electronical leakage in pixels or that the camera for another reason interprets around the double amountof pixels than it should. To get better results with multiple �shing lines several LEDs/lasers could be used so thatevery �shing line get the same amount of light. One consequence with several LEDs/lasers is that the alignment ofthe setup gets more complicated.

5 Conclusion

The main goal of this project was to develop a method to improve the time resolution and e�ciency of the pellettracking system. Challenges with making trustworthy measurements were stability in the setup, di�culties withalignment and optimizing of exposure cycles.

To overcome stability issues, a more stable and robust module that also will ease adjustment of alignment isunder construction. A well-aligned setup can be con�rmed in two ways. Firstly by con�rming that the camerasdetect pellet signals for a about 300µm-height change of the laser or the camera and secondly that the focus intervalis about 100µm. A mathematical model was developed that calculates class-distributions for varying exposure cyclesand shifts can be used to predict the results from a measurement with pellets. The model can be used for testingan appropriate exposure cycle before running it with pellets. Investigations of electronic e�ects should be made tofurther improve the tracking system. In addition, an appropriate laser power should be chosen since the e�ects ofboth too low and too high power are unreadable or misleading results.

13

6 References

1. Personal communication with Calén, H., Supervisor, Uppsala University, Department of Physics and Astron-omy, division for Nuclear Physics

2. Pyszniak, A. 2014, Development and Applications of Tracking of Pellet Streams, Uppsala Dissertations fromthe faculty of Science and Technology

14

Appendix A

MATLAB-code

MATLAB was used to develop the matematical model for the distribution of entries in the classes ABsm, BnxAand BnoA.

matdata.m

This �le loads and plots the values from a chosen measurement (pellet och bench test setup) against the delay. Theloaded text �les are built up in columns with the delay, the classes ABsm/B, BnxA/B, BnoA/B in the �rst, second,third and fourth column respectively.

c l e a r a l l

% f i l e = '150506_C13_E10 . txt ' ; % Sparse measurements% f i l e = '150506_C20_E15 . txt ' ; % Sparse measurements% f i l e = '150506_C20_E10 . txt ' ; % Sparse measurements% f i l e = '150508_C13_E5 . 5 . txt ' ; % dead>exp% f i l e = '150508_C13_E7. txt ' ;% f i l e = '150508_C13_E8 . 5 . txt ' ;% f i l e = '150518_C13_E10_W2. 5 . txt ' ;% f i l e = '150519_C13_E8. 5_W4. 5 . txt ' ;f i l e = '150526_C13_E7_W4. 5 . txt ' ;comma2point_overwrite ( f i l e )A=load ( f i l e ) ;cyc = 13 ; %cyc l e timeexp = 7 ; %exposurepu l s e = 4 . 5 ; %pu l s e l engthf i g = 1 ;

u = 200 ; %r e s o l u t i o nDelay = A( : , 1 ) ;ABsm = A( : , 2 ) ;BnxA = A( : , 3 ) ;BnoA = A( : , 4 ) ;norm = ABsm(1)+BnxA(1);%+BnoA( 1 ) ;% Divided by t o t a l e n t r i e s in B

delay=l i n s p a c e (0 , cyc , u ) ' ;

sm=ze ro s (u , 1 ) ; nx=ze ro s (u , 1 ) ; no=ze ro s (u , 1 ) ;f o r k=1:u

[ sm(k ) , nx (k ) , no (k ) ] = e n t r i e s ( cyc , exp , pulse , de lay (k ) ) ;endsm=norm .* sm ; nx=norm .* nx ; no=norm .* no ;

s e t ( 0 , ' DefaultAxesFontSize ' , 2 4 )s e t ( 0 , ' DefaultAxesFontName ' , ' Times New Roman ' )s e t ( 0 , ' defaultLineLineWidth ' , 2 . 5 ) ;s e t ( f i g u r e ( f i g ) , ' Pos i t ion ' , [ 50 50 800 400 ] )

f i g u r e ( f i g )

15

p lo t (Delay ,ABsm, ' b* ' , Delay ,BnxA, ' g * ' , Delay ,BnoA, ' r * ' , . . .delay , sm , 'b− ' , delay , nx , ' g− ' , delay , no , ' r − ' ) ;

l egend ( 'ABsm − p e l l e t ' , 'BnxA − p e l l e t ' , 'BnoA − p e l l e t ' , . . .'ABsm − theory ' , 'BnxA − theory ' , 'BnoA − theory ' , . . .' Location ' , ' e a s tou t s id e ' )

g l oba l mint i t l e ( [ ' Cycle : ' , num2str ( cyc ) , ' \mus ' . . .

' Exposure : ' , num2str ( exp ) , ' \mus ' . . .' Pulse : ' , num2str ( pu l s e ) , ' \mus ' . . .'Min . s i g n a l : ' , num2str (min ) , ' \mus ' ] ) ;

y l ab e l ( ' Percentage ' )x l ab e l ( ' Delay [ \mus ] ' )xl im ( [ 0 , cyc ] ) ;yl im ( [ −0 . 0 0 5 , 1 ] ) ;

entries.m

The function entries.m calculates the distribution of entries in each class.

f unc t i on [ sm , nx , no ] = e n t r i e s ( cyc , exp , pulse , de lay )

g l oba l minmin = 0 . 2 5 ; %minimum time a s i g n a l need to occur in order to be seen .

i f min < pu l s e /2y = ( pu l s e/2−min ) ;exp = exp+2*y ;

enddead = cyc−exp ;

i f y/dead > 0 . 5 ;y=0.5*dead ;

end

i f dead<=exp

i f delay<=dead−ysm = 1−( de lay /exp ) ;nx = 0 ;no = delay /exp ;

e l s e i f delay<=deadsm = 1−( de lay /exp ) ;nx = 0 ;no = delay /exp ;

e l s e i f delay<=expsm = 1−( de lay /exp ) ;nx = ( delay−dead )/ exp ;

16

no = dead/exp ;

e l s e i f delay<=exp+ysm = 0 ;nx = ( delay−dead )/ exp ;no = ( cyc−delay )/ exp ;

e l s e i f delay>exp+ysm = 0 ;nx = ( delay−dead )/ exp ;no = ( cyc−delay )/ exp ;

endendend

pellet_vs_�shingline.m

This �le plots the measured values from a pellet run, the measured values from the bench test up and calculatedvalues against the delay.

% p e l l e t = '150508_C13_E7. txt ' ;% f i s h i n g l i n e = '150526_C13_E7_W2. 5 . txt ' ;p e l l e t = '150508_C13_E8 . 5 . txt ' ;f i s h i n g l i n e = '150519_C13_E8. 5_W2. 5 . txt ' ;

% comma2point_overwrite ( p e l l e t )% comma2point_overwrite ( f i s h l i n e )A=load ( p e l l e t ) ;B=load ( f i s h i n g l i n e ) ;

cyc = 13 ; %cyc l e timeexp = 8 . 5 ; %exposurepu l se_las = 2 . 5 ;pu l s e = 3 ; %pu l se l ength

DelayP = A( : , 1 ) ;ABsmP = A( : , 2 ) ;BnxAP = A( : , 3 ) ;BnoAP = A( : , 4 ) ;DelayF = B( : , 1 ) ;ABsmF = B( : , 2 ) ;BnxAF = B( : , 3 ) ;BnoAF = B( : , 4 ) ;

norm = ABsmP(1)+BnxAP(1);%+BnoA( 1 ) ;

u = 200 ; %r e s o l u t i o nde lay=l i n s p a c e (0 , cyc , u ) ' ;

sm=ze ro s (u , 1 ) ; nx=ze ro s (u , 1 ) ; no=ze ro s (u , 1 ) ;f o r k=1:u

17

[ sm(k ) , nx (k ) , no (k ) ] = ent2 ( cyc , exp , pulse , de lay (k ) ) ;endsm=norm .* sm ; nx=norm .* nx ; no=norm .* no ;

s e t ( 0 , ' DefaultAxesFontSize ' , 2 4 )s e t ( 0 , ' DefaultAxesFontName ' , ' Times New Roman ' )s e t ( 0 , ' defaultLineLineWidth ' , 2 . 5 ) ;s e t ( f i g u r e ( 1 ) , ' Pos i t ion ' , [ 50 50 800 400 ] )

f i g u r e (1 )p l o t (DelayP ,ABsmP, ' b* ' , DelayP ,BnxAP, ' g * ' , DelayP ,BnoAP, ' r * ' , . . .

DelayF ,ABsmF, ' bo ' , DelayF ,BnxAF, ' go ' , DelayF ,BnoAF, ' ro ' , . . .delay , sm , 'b− ' , delay , nx , ' g− ' , delay , no , ' r − ' ) ;

l egend ( 'ABsm − p e l l e t ' , 'BnxA − p e l l e t ' , 'BnoA − p e l l e t ' , . . .'ABsm − f i s h i n g l i n e ' , 'BnxA − f i s h i n g l i n e ' , 'BnoA − f i s h i n g l i n e ' , . . .' Location ' , ' e a s tou t s id e ' , . . .'ABsm − theory ' , 'BnxA − theory ' , 'BnoA − theory ' )

g l oba l min

t i t l e ( [ ' Cycle : ' , num2str ( cyc ) , ' \mus ' . . .' Exposure : ' , num2str ( exp ) , ' \mus ' . . .' Pulse l a s e r : ' , num2str ( pu l se_las ) , ' \mus ' . . .' Pulse c a l c : ' , num2str ( pu l s e ) , ' \mus ' . . .'Min . s i g n a l : ' , num2str (min ) , ' \mus ' ] ) ;

y l ab e l ( ' Percentage ' )x l ab e l ( ' Delay [ \mus ] ' )xl im ( [ 0 , cyc ] ) ;yl im ( [ 0 , 1 ] ) ;

18

Appendix B

Diagrams

Measured data and model expectations.

Pellet-data

Measured data from pellet-runs compared to the model using pulse length 2.5µs and 3µs. By comparing the graphsthe e�ects of di�erent exposure time and di�erent choice of pulse length are shown.

Figure 16: Measured values from a pellet run with cycle time 13µs and exposure time 5.5µs and corresponding calculated/ap-proximated values for a pulse length of 2.5µs to the left and3µs to the right.

Figure 17: Measured values from a pellet run with cycle time 13µs and exposure time 7µs and corresponding calculated/ap-proximated values for a pulse length of 2.5µs to the left and3µs to the right.

Figure 18: Measured values from a pellet run with cycle time 13µs and exposure time 8.5µs and corresponding calculated/ap-proximated values for a pulse length of 2.5µs to the left and3µs to the right.

19

Fishing-line-data

Measured data from bench test setup-runs compared to the model for exposure time 7µs and 8µs and pulse length1.5µs, 2.5µs, 3.5µs and 4.5µs and the corresponding calculated values for a 0.5µs longer pulse. By comparingthe graphs the e�ects of di�erent exposure time and di�erent pulse length are shown.

Figure 19: Measured values for �shing line with a exposure cycle of 13µs, exposure time of 7µs, to the left and 8.5µs, to theright. The laser pulse is 1.5µs, 2.5µs, 3.5µs and 4.5µs and the corresponding calculated values for a pulse length of 2µs,3µs, 4µs respectively 5µs.

20