Design and characterization of large area position sensitive radiation detectors

Planar, large area, position sensitive silicon detectors are widely utilized in high energy physics research and in medical, computed tomography (CT). This thesis describes author's research work relating to development of such detector components. The key motivation and objective for the research work has been the development of novel, position sensitive detectors improving the performance of the instruments they are intended for. Silicon strip detectors are the key components of barrel-shaped tracking instruments which are typically the innermost structures of high energy physics experimental stations. Particle colliders such as the former LEP collider or present LHC produce particle collisions and the silicon strip detector based trackers locate the trajectories of particles emanating from such collisions. Medical CT has become a regular part of everyday medical care in all developed countries. CT scanning enables x-ray imaging of all parts of the human body with an outstanding structural resolution and contrast. Brain, chest and abdomen slice images with a resolution of 0.5 mm are possible and latest CT machines are able to image whole human heart between heart beats. The two application areas are presented shortly and the radiation detection properties of planar silicon detectors are discussed. Fabrication methods and preamplifier electronics of the planar detectors are presented. Designs of the developed, large area silicon detectors are presented and measurement results of the key operating parameters are discussed. Static and dynamic performance of the developed silicon strip detectors are shown to be very satisfactory for experimental physics applications. Results relating to the developed, novel CT detector chips are found to be very promising for further development and all key performance goals are met.

Fabrication and characterization of silicon position sensitive particle detectors

Position sensitive particle detectors are needed in high energy physics research. This thesis describes the development of fabrication processes and characterization techniques of silicon microstrip detectors used in the work for searching elementary particles in the European center for nuclear research, CERN. The detectors give an electrical signal along the particles trajectory after a collision in the particle accelerator. The trajectories give information about the nature of the particle in the struggle to reveal the structure of the matter and the universe. Detectors made of semiconductors have a better position resolution than conventional wire chamber detectors. Silicon semiconductor is overwhelmingly used as a detector material because of its cheapness and standard usage in integrated circuit industry. After a short spread sheet analysis of the basic building block of radiation detectors, the pn junction, the operation of a silicon radiation detector is discussed in general. The microstrip detector is then introduced and the detailed structure of a double-sided ac-coupled strip detector revealed. The fabrication aspects of strip detectors are discussedstarting from the process development and general principles ending up to the description of the double-sided ac-coupled strip detector process. Recombination and generation lifetime measurements in radiation detectors are discussed shortly. The results of electrical tests, ie. measuring the leakage currents and bias resistors, are displayed. The beam test setups and the results, the signal to noise ratio and the position accuracy, are then described. It was found out in earlier research that a heavy irradiation changes the properties of radiation detectors dramatically. A scanning electron microscope method was developed to measure the electric potential and field inside irradiated detectorsto see how a high radiation fluence changes them. The method and the most important results are discussed shortly.

Amorphous silicon e 3D sensors applied to object detection

Nowadays, existing 3D scanning cameras and microscopes in the market use digital or discrete sensors, such as CCDs or CMOS for object detection applications. However, these combined systems are not fast enough for some application scenarios since they require large data processing resources and can be cumbersome. Thereby, there is a clear interest in exploring the possibilities and performances of analogue sensors such as arrays of position sensitive detectors with the final goal of integrating them in 3D scanning cameras or microscopes for object detection purposes. The work performed in this thesis deals with the implementation of prototype systems in order to explore the application of object detection using amorphous silicon position sensors of 32 and 128 lines which were produced in the clean room at CENIMAT-CEMOP. During the first phase of this work, the fabrication and the study of the static and dynamic specifications of the sensors as well as their conditioning in relation to the existing scientific and technological knowledge became a starting point. Subsequently, relevant data acquisition and suitable signal processing electronics were assembled. Various prototypes were developed for the 32 and 128 array PSD sensors. Appropriate optical solutions were integrated to work together with the constructed prototypes, allowing the required experiments to be carried out and allowing the achievement of the results presented in this thesis. All control, data acquisition and 3D rendering platform software was implemented for the existing systems. All these components were combined together to form several integrated systems for the 32 and 128 line PSD 3D sensors. The performance of the 32 PSD array sensor and system was evaluated for machine vision applications such as for example 3D object rendering as well as for microscopy applications such as for example micro object movement detection. Trials were also performed involving the 128 array PSD sensor systems. Sensor channel non-linearities of approximately 4 to 7% were obtained. Overall results obtained show the possibility of using a linear array of 32/128 1D line sensors based on the amorphous silicon technology to render 3D profiles of objects. The system and setup presented allows 3D rendering at high speeds and at high frame rates. The minimum detail or gap that can be detected by the sensor system is approximately 350 μm when using this current setup. It is also possible to render an object in 3D within a scanning angle range of 15º to 85º and identify its real height as a function of the scanning angle and the image displacement distance on the sensor. Simple and not so simple objects, such as a rubber and a plastic fork, can be rendered in 3D properly and accurately also at high resolution, using this sensor and system platform. The nip structure sensor system can detect primary and even derived colors of objects by a proper adjustment of the integration time of the system and by combining white, red, green and blue (RGB) light sources. A mean colorimetric error of 25.7 was obtained. It is also possible to detect the movement of micrometer objects using the 32 PSD sensor system. This kind of setup offers the possibility to detect if a micro object is moving, what are its dimensions and what is its position in two dimensions, even at high speeds. Results show a non-linearity of about 3% and a spatial resolution of < 2µm.

Monte Carlo Simulations of Novel Scintillator Detectors and Dosimetry Calculations

Monte Carlo (MC) simulation techniques are becoming very common in the Medical Physicists community. MC can be used for modeling Single Photon Emission Computed Tomography (SPECT) and for dosimetry calculations. 188Re, is a promising candidate for radiotherapeutic production and understanding the mechanisms of the radioresponse of tumor cells "in vitro" is of crucial importance as a first step before "in vivo" studies. The dosimetry of 188Re, used to target different lines of cancer cells, has been evaluated by the MC code GEANT4. The simulations estimate the average energy deposition/per event in the biological samples. The development of prototypes for medical imaging, based on LaBr3:Ce scintillation crystals coupled with a position sensitive photomultiplier, have been studied using GEANT4 simulations. Having tested, in the simulation, surface treatments different from the one applied to the crystal used in our experimental measurements, we found out that the Energy Resolution (ER) and the Spatial Resolution (SR) could be improved, in principle, by machining in a different way the lateral surfaces of the crystal. We have then studied a system able to acquire both echographic and scintigraphic images to let the medical operator obtain the complete anatomic and functional information for tumor diagnosis. The scintigraphic part of the detector is simulated by GEANT4 and first attempts to reconstruct tomographic images have been made using as method of reconstruction a back-projection standard algorithm. The proposed camera is based on slant collimators and LaBr3:Ce crystals. Within the Field of View (FOV) of the camera, it possible to distinguish point sources located in air at a distance of about 2 cm from each other. In particular conditions of uptake, tumor depth and dimension, the preliminary results show that the Signal to Noise Ratio (SNR) values obtained are higher than the standard detection limit.

Emulsion detectors for the antihydrogen detection in AEgIS

The AEgIS experiment at CERN aims to perform the first direct measurement of gravitational interaction between matter and antimatter by measuring the deviation of a cold antihydrogen beam in the Earth gravitational field. The design of the experiment has been recently updated to include emulsion films as position sensitive detector. The submicrometric position accuracy of emulsions leads indeed to a significant improvement of the experimental sensitivity. We present results of preliminary tests and discuss perspectives for the final measurement.

Colour filtering in a-SiC : H based p-i-n-p-i-n cells: A trade-off between bias polarity and absorption regions

A large area colour imager optically addressed is presented. The colour imager consists of a thin wide band gap p-i-n a-SiC:H filtering element deposited on the top of a thick large area a-SiC:H(-p)/a-Si:H(-i)/a-SiC:H(-n) image sensor, which reveals itself an intrinsic colour filter. In order to tune the external applied voltage for full colour discrimination the photocurrent generated by a modulated red light is measured under different optical and electrical bias. Results reveal that the integrated device behaves itself as an imager and a filter giving information not only on the position where the optical image is absorbed but also on it wavelength and intensity. The amplitude and sign of the image signals are electrically tuneable. In a wide range of incident fluxes and under reverse bias, the red and blue image signals are opposite in sign and the green signal is suppressed allowing blue and red colour recognition. The green information is obtained under forward bias, where the blue signal goes down to zero and the red and green remain constant. Combining the information obtained at this two applied voltages a RGB colour image picture can be acquired without the need of the usual colour filters or pixel architecture. A numerical simulation supports the colour filter analysis.

Polarization and correlation phenomena in the radiative electron capture by bare highly-charged ions

In dieser Arbeit wird die Wechselwirkung zwischen einem Photon und einem Elektron im starken Coulombfeld eines Atomkerns am Beispiel des radiativen Elektroneneinfangs beim Stoß hochgeladener Teilchen untersucht. In den letzten Jahren wurde dieser Ladungsaustauschprozess insbesondere für relativistische Ion–Atom–Stöße sowohl experimentell als auch theoretisch ausführlich erforscht. In Zentrum standen dabei haupsächlich die totalen und differentiellen Wirkungsquerschnitte. In neuerer Zeit werden vermehrt Spin– und Polarisationseffekte sowie Korrelationseffekte bei diesen Stoßprozessen diskutiert. Man erwartet, dass diese sehr empfindlich auf relativistische Effekte im Stoß reagieren und man deshalb eine hervorragende Methode zu deren Bestimmung erhält. Darüber hinaus könnten diese Messungen auch indirekt dazu führen, dass man die Polarisation des Ionenstrahls bestimmen kann. Damit würden sich neue experimentelle Möglichkeiten sowohl in der Atom– als auch der Kernphysik ergeben. In dieser Dissertation werden zunächst diese ersten Untersuchungen zu den Spin–, Polarisations– und Korrelationseffekten systematisch zusammengefasst. Die Dichtematrixtheorie liefert hierzu die geeignete Methode. Mit dieser Methode werden dann die allgemeinen Gleichungen für die Zweistufen–Rekombination hergeleitet. In diesem Prozess wird ein Elektron zunächst radiativ in einen angeregten Zustand eingefangen, der dann im zweiten Schritt unter Emission des zweiten (charakteristischen) Photons in den Grundzustand übergeht. Diese Gleichungen können natürlich auf beliebige Mehrstufen– sowie Einstufen–Prozesse erweitert werden. Im direkten Elektroneneinfang in den Grundzustand wurde die ”lineare” Polarisation der Rekombinationsphotonen untersucht. Es wurde gezeigt, dass man damit eine Möglichkeit zur Bestimmung der Polarisation der Teilchen im Eingangskanal des Schwerionenstoßes hat. Rechnungen zur Rekombination bei nackten U92+ Projektilen zeigen z. B., dass die Spinpolarisation der einfallenden Elektronen zu einer Drehung der linearen Polarisation der emittierten Photonen aus der Streuebene heraus führt. Diese Polarisationdrehung kann mit neu entwickelten orts– und polarisationsempfindlichen Festkörperdetektoren gemessen werden. Damit erhält man eine Methode zur Messung der Polarisation der einfallenden Elektronen und des Ionenstrahls. Die K–Schalen–Rekombination ist ein einfaches Beispiel eines Ein–Stufen–Prozesses. Das am besten bekannte Beispiel der Zwei–Stufen–Rekombination ist der Elektroneneinfang in den 2p3/2–Zustand des nackten Ions und anschließendem Lyman–1–Zerfall (2p3/2 ! 1s1/2). Im Rahmen der Dichte–Matrix–Theorie wurden sowohl die Winkelverteilung als auch die lineare Polarisation der charakteristischen Photonen untersucht. Beide (messbaren) Größen werden beträchtlich durch die Interferenz des E1–Kanals (elektrischer Dipol) mit dem viel schwächeren M2–Kanal (magnetischer Quadrupol) beeinflusst. Für die Winkelverteilung des Lyman–1 Zerfalls im Wasserstoff–ähnlichen Uran führt diese E1–M2–Mischung zu einem 30%–Effekt. Die Berücksichtigung dieser Interferenz behebt die bisher vorhandene Diskrepanz von Theorie und Experiment beim Alignment des 2p3/2–Zustands. Neben diesen Ein–Teichen–Querschnitten (Messung des Einfangphotons oder des charakteristischen Photons) wurde auch die Korrelation zwischen den beiden berechnet. Diese Korrelationen sollten in X–X–Koinzidenz–Messungen beobbachtbar sein. Der Schwerpunkt dieser Untersuchungen lag bei der Photon–Photon–Winkelkorrelation, die experimentell am einfachsten zu messen ist. In dieser Arbeit wurden ausführliche Berechnungen der koinzidenten X–X–Winkelverteilungen beim Elektroneneinfang in den 2p3/2–Zustand des nackten Uranions und beim anschließenden Lyman–1–Übergang durchgeführt. Wie bereits erwähnt, hängt die Winkelverteilung des charakteristischen Photons nicht nur vom Winkel des Rekombinationsphotons, sondern auch stark von der Spin–Polarisation der einfallenden Teilchen ab. Damit eröffnet sich eine zweite Möglichkeit zur Messung der Polaristion des einfallenden Ionenstrahls bzw. der einfallenden Elektronen.

Transverse pseudo-nonlinear effects measured in solid-state laser materials using a sensitive time-resolved technique

We present a detailed study of the Baryscan technique, a new efficient alternative to the widespread Z-scan technique which has been demonstrated [Opt. Lett. 36:8, 2011] to reach among the highest sensitivity levels. This method is based upon the measurement of optical nonlinearities by means of beam centroid displacements with a position sensitive detector and is able to deal with any kind of lensing effect. This technique is applied here to measure pump-induced electronic refractive index changes (population lens), which can be discriminated from parasitic thermal effects by using a time-resolved Baryscan experiment. This method is validated by evaluating the polarizability variation at the origin of the population lens observed in the reference Cr3+:GSGG laser material.

Development of an X-ray spectrometric system and feasibility tests of Silicon Drift Detector for medical and space applications

The thesis work concerns X-ray spectrometry for both medical and space applications and is divided into two sections. The first section addresses an X-ray spectrometric system designed to study radiological beams and is devoted to the optimization of diagnostic procedures in medicine. A parametric semi-empirical model capable of efficiently reconstructing diagnostic X-ray spectra in 'middle power' computers was developed and tested. In addition, different silicon diode detectors were tested as real-time detectors in order to provide a real-time evaluation of the spectrum during diagnostic procedures. This project contributes to the field by presenting an improved simulation of a realistic X-ray beam emerging from a common X-ray tube with a complete and detailed spectrum that lends itself to further studies of added filtration, thus providing an optimized beam for different diagnostic applications in medicine. The second section describes the preliminary tests that have been carried out on the first version of an Application Specific Integrated Circuit (ASIC), integrated with large area position-sensitive Silicon Drift Detector (SDD) to be used on board future space missions. This technology has been developed for the ESA project: LOFT (Large Observatory for X-ray Timing), a new medium-class space mission that the European Space Agency has been assessing since February of 2011. The LOFT project was proposed as part of the Cosmic Vision Program (2015-2025).

Development of nuclear emulsions with 1 μm spatial resolution for the AEgIS experiment

The main goal of the AEgIS experiment at CERN is to test the weak equivalence principle for antimatter. We will measure the Earth ' s gravitational acceleration g with antihydrogen atoms being launched in a horizontal vacuum tube and traversing a moiré de fl ectometer. We intend to use a position sensitive device made of nuclear emulsions (combined with a time-of- fl ight detector such as silicon μ strips) to measure precisely their annihilation points at the end of the tube. The goal is to determine g with a 1% relative accuracy. In 2012 we tested emulsion fi lms in vacuum and at room temperature with low energy antiprotons from the CERN antiproton decelerator. First results on the expected performance for AEgIS are presented

Measuring the gravitational free-fall of antihydrogen

Antihydrogen holds the promise to test, for the first time, the universality of freefall with a system composed entirely of antiparticles. The AEgIS experiment at CERN’s antiproton decelerator aims to measure the gravitational interaction between matter and antimatter by measuring the deflection of a beam of antihydrogen in the Earths gravitational field (g). The principle of the experiment is as follows: cold antihydrogen atoms are synthesized in a Penning-Malberg trap and are Stark accelerated towards a moir´e deflectometer, the classical counterpart of an atom interferometer, and annihilate on a position sensitive detector. Crucial to the success of the experiment is the spatial precision of the position sensitive detector.We propose a novel free-fall detector based on a hybrid of two technologies: emulsion detectors, which have an intrinsic spatial resolution of 50 nm but no temporal information, and a silicon strip / scintillating fiber tracker to provide timing and positional information. In 2012 we tested emulsion films in vacuum with antiprotons from CERN’s antiproton decelerator. The annihilation vertices could be observed directly on the emulsion surface using the microscope facility available at the University of Bern. The annihilation vertices were successfully reconstructed with a resolution of 1–2 μmon the impact parameter. If such a precision can be realized in the final detector, Monte Carlo simulations suggest of order 500 antihydrogen annihilations will be sufficient to determine gwith a 1 % accuracy. This paper presents current research towards the development of this technology for use in the AEgIS apparatus and prospects for the realization of the final detector.

Dual-Phase Liquid Xenon Detectors for Dark Matter Searches

Dual-phase time projection chambers (TPCs) filled with the liquid noble gas xenon (LXe) are currently the most sensitive detectors searching for interactions of WIMP dark matter in a laboratory-based experiment. This is achieved by combining a large, monolithic dark matter target of a very low background with the capability to localize the interaction vertex in three dimensions, allowing for target fiducialization and multiple-scatter rejection. The background in dual-phase LXe TPCs is further reduced by the simultaneous measurement of the scintillation and ionization signal from a particle interaction, which is used to distinguish signal from background signatures. This article reviews the principle of dual-phase LXe TPCs, and provides an overview about running as well as future experimental efforts.

Photothermal Investigations on Certain Plasma Polymerized Thin Films and Near IR Overtone Studies of Some Organic Molecules

Photothermal effect refers to heating of a sample due to the absorption of electromagnetic radiation. Photothermal (PT) heat generation which is an example of energy conversion has in general three kinds of applications. 1. PT material probing 2. PT material processing and 3. PT material destruction. The temperatures involved increases from 1-. 3. Of the above three, PT material probing is the most important in making significant contribution to the field of science and technology. Photothermal material characterization relies on high sensitivity detection techniques to monitor the effects caused by PT material heating of a sample. Photothermal method is a powerful high sensitivity non-contact tool used for non-destructive thermal characterization of materials. The high sensitivity of the photothermal methods has led to its application for analysis of low absorbance samples. Laser calorimetry, photothermal radiometry, pyroelectric technique, photoacoustic technique, photothermal beam deflection technique, etc. come under the broad class ofphotothermal techniques. However the choice of a suitable technique depends upon the nature of the sample, purpose of measurement, nature of light source used, etc. The present investigations are done on polymer thin films employing photothermal beam deflection technique, for the successful determination of their thermal diffusivity. Here the sample is excited by a He-Ne laser (A = 6328...\ ) which acts as the pump beam. Due to the refractive index gradient established in the sample surface and in the adjacent coupling medium, another optical beam called probe beam (diode laser, A= 6500A ) when passed through this region experiences a deflection and is detected using a position sensitive detector and its output is fed to a lock-in amplifier from which the amplitude and phase of the deflection can be directly obtained. The amplitude and phase of the signal is suitably analysed for determining the thermal diffusivity.The production of polymer thin film samples has gained considerable attention for the past few years. Plasma polymerization is an inexpensive tool for fabricating organic thin films. It refers to formation of polymeric materials under the influence of plasma, which is generated by some kind of electric discharge. Here plasma of the monomer vapour is generated by employing radio frequency (MHz) techniques. Plasma polymerization technique results in homogeneous, highly adhesive, thermally stable, pinhole free, dielectric, highly branched and cross-linked polymer films. The possible linkage in the formation of the polymers is suggested by comparing the FTIR spectra of the monomer and the polymer.Near IR overtone investigations on some organic molecules using local mode model are also done. Higher vibrational overtones often provide spectral simplification and greater resolution of peaks corresponding to nonequivalent X-H bonds where X is typically C, N or O. Vibrational overtone spectroscopy of molecules containing X-H oscillators is now a well established tool for molecular investigations. Conformational and steric differences between bonds and structural inequivalence ofCH bonds (methyl, aryl, acetylenic, etc.) are resolvable in the higher overtone spectra. The local mode model in which the X-H oscillators are considered to be loosely coupled anharmonic oscillators has been widely used for the interpretation of overtone spectra. If we are exciting a single local oscillator from the vibrational ground state to the vibrational state v, then the transition energy of the local mode overtone is given by .:lE a......v = A v + B v2 • A plot of .:lE / v versus v will yield A, the local mode frequency as the intercept and B, the local mode diagonal anharmonicity as the slope. Here A - B gives the mechanical frequency XI of the oscillator and B = X2 is the anharmonicity of the bond. The local mode parameters XI and X2 vary for non-equivalent X-H bonds and are sensitive to the inter and intra molecular environment of the X-H oscillator.

Photothermal and photoacoustic investigations on certain polymers and semi conducting materials

Material synthesizing and characterization has been one of the major areas of scientific research for the past few decades. Various techniques have been suggested for the preparation and characterization of thin films and bulk samples according to the industrial and scientific applications. Material characterization implies the determination of the electrical, magnetic, optical or thermal properties of the material under study. Though it is possible to study all these properties of a material, we concentrate on the thermal and optical properties of certain polymers. The thermal properties are detennined using photothermal beam deflection technique and the optical properties are obtained from various spectroscopic analyses. In addition, thermal properties of a class of semiconducting compounds, copper delafossites, arc determined by photoacoustic technique.Photothermal technique is one of the most powerful tools for non-destructive characterization of materials. This forms a broad class of technique, which includes laser calorimetry, pyroelectric technique, photoacollstics, photothermal radiometric technique, photothermal beam deflection technique etc. However, the choice of a suitable technique depends upon the nature of sample and its environment, purpose of measurement, nature of light source used etc. The polynler samples under the present investigation are thermally thin and optically transparent at the excitation (pump beam) wavelength. Photothermal beam deflection technique is advantageous in that it can be used for the detennination of thermal diffusivity of samples irrespective of them being thermally thick or thennally thin and optically opaque or optically transparent. Hence of all the abovementioned techniques, photothemlal beam deflection technique is employed for the successful determination of thermal diffusivity of these polymer samples. However, the semi conducting samples studied are themlally thick and optically opaque and therefore, a much simpler photoacoustic technique is used for the thermal characterization.The production of polymer thin film samples has gained considerable attention for the past few years. Different techniques like plasma polymerization, electron bombardment, ultra violet irradiation and thermal evaporation can be used for the preparation of polymer thin films from their respective monomers. Among these, plasma polymerization or glow discharge polymerization has been widely lIsed for polymer thin fi Im preparation. At the earlier stages of the discovery, the plasma polymerization technique was not treated as a standard method for preparation of polymers. This method gained importance only when they were used to make special coatings on metals and began to be recognized as a technique for synthesizing polymers. Thc well-recognized concept of conventional polymerization is based on molecular processcs by which thc size of the molecule increases and rearrangemcnt of atoms within a molecule seldom occurs. However, polymer formation in plasma is recognized as an atomic process in contrast to the above molecular process. These films are pinhole free, highly branched and cross linked, heat resistant, exceptionally dielectric etc. The optical properties like the direct and indirect bandgaps, refractive indices etc of certain plasma polymerized thin films prepared are determined from the UV -VIS-NIR absorption and transmission spectra. The possible linkage in the formation of the polymers is suggested by comparing the FTIR spectra of the monomer and the polymer. The thermal diffusivity has been measured using the photothermal beam deflection technique as stated earlier. This technique measures the refractive index gradient established in the sample surface and in the adjacent coupling medium, by passing another optical beam (probe beam) through this region and hence the name probe beam deflection. The deflection is detected using a position sensitive detector and its output is fed to a lock-in-amplifIer from which the amplitude and phase of the deflection can be directly obtained. The amplitude and phase of the deflection signal is suitably analyzed for determining the thermal diffusivity.Another class of compounds under the present investigation is copper delafossites. These samples in the form of pellets are thermally thick and optically opaque. Thermal diffusivity of such semiconductors is investigated using the photoacoustic technique, which measures the pressure change using an elcctret microphone. The output of the microphone is fed to a lock-in-amplificr to obtain the amplitude and phase from which the thermal properties are obtained. The variation in thermal diffusivity with composition is studied.

Damage threshold determination of bulk polymer samples using pulsed photothermal deflection technique

Photothermal deflection technique was used for determining the laser damage threshold of polymer samples of teflon (PTFE) and nylon. The experiment was conducted using a Q-switched Nd-YAG laser operating at its fundamental wavelength (1-06μm, pulse width 10 nS FWHM) as irradiation source and a He-Ne laser as the probe beam, along with a position sensitive detector. The damage threshold values determined by photothermal deflection method were in good agreement with those determined by other methods.