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Ultrasonic Computed Tomography: Pushing the Boundaries of the Ultrasonic Inspection of Forgings

Authors:
  • Vrana GmbH - NDE Consulting and Solutions

Abstract and Figures

Forgings, being usually one of the most critical components especially in power generation machinery, require intensive volumetric inspection to guarantee a sufficient lifetime. This is usually accomplished by manual or automated ultrasonic testing. We are reporting about a game changer in ultrasonic testing: Ultrasonic Computed Tomography uses analytics (i.e. a mathematical algorithm) to reconstruct the volume (In fact it uses a linearized diffraction tomographic approach for the solution of the inverse problem). This does not only allow to display indications spatially and visually correct in the 3D volume, but also improves the signal to noise ratio significantly, allowing an increase of sensitivity by up to an order of magnitude. The method is based on the Synthetic Aperture Focusing Technique (SAFT). The applied software is a brand-new implementation of SAFT with a strong focus for a large scale industrial application: the complete 2D as well as 3D reconstruction of ultrasonic inspections of heavy rotor forgings. This paper shows the working principle of the method along with the first results and computation times. Ultrasonic Computed Tomography was also awarded by the Werner von Siemens Award as one of the Top 15 ingenuity programs.
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JOHANNES VRANA1, KARSTEN SCHÖRNER2, HUBERT MOOSHOFER2,
KARSTEN KOLK2, ALEXANDER ZIMMER3, KARL FENDT4
ULTRASONIC COMPUTED TOMOGRAPHY PUSHING THE
BOUNDARIES OF THE ULTRASONIC INSPECTION OF FORGINGS
Abstract
Forgings, being usually one of the most critical components especially in power
generation machinery, require intensive volumetric inspection to guarantee a sufficient
lifetime. This is usually accomplished by manual or automated ultrasonic testing.
We are reporting about a game changer in ultrasonic testing: Ultrasonic Computed
Tomography uses analytics (i.e. a mathematical algorithm) to reconstruct the volume (In fact
it uses a linearized diffraction tomographic approach for the solution of the inverse problem).
This does not only allow to display indications spatially and visually correct in the 3D
volume, but also improves the signal to noise ratio significantly, allowing an increase of
sensitivity by up to an order of magnitude. The method is based on the Synthetic Aperture
Focusing Technique (SAFT). The applied software is a brand-new implementation of SAFT
with a strong focus for a large scale industrial application: the complete 2D as well as 3D
reconstruction of ultrasonic inspections of heavy rotor forgings.
This paper shows the working principle of the method along with the first results and
computation times. Ultrasonic Computed Tomography was also awarded by the Werner von
Siemens Award as one of the Top 15 ingenuity programs.
Keywords
NDE, NDT, Ultrasonic Testing, UT, Synthetic Aperture Focusing Technique, SAFT,
Reconstruction, CT, Computed Tomography
1. Introduction
Ultrasonic testing of forgings started right after the commercial availability of the first
ultrasonic systems around 1950 [1, 2, 3] and became one of the most important tools to
guarantee a sufficient lifetime (see Fig. 1). Material and NDE Engineers got a view into the
components and Engineers learned how to interpret signals and how to classify indications.
This information feedback from the final parts also helped improving the melting, heat
treatment and forging processes.
In the 1960s fracture mechanics was introduced and starting around 1970 sizing of
indications became a requirement for most large forgings. For indications larger than the
beam profile, sizing by probe travel (echo dynamic sizing, e.g. -6 dB drop method) is used
and for indications smaller than the beam profile area amplitude based sizing methods are
used (like DAC or DGS). Those methods compare the reflectivity of indications with the
reflectivity of artificial reflectors like Flat Bottom Holes, Disc Shaped Reflectors, or simply
1 VRANA GMBH
2 SIEMENS AG
3 SAARSCHMIEDE GMBH
4 FRIEDRICH-ALEXANDER-UNIVERSITÄT ERLANGEN-NÜRNBERG
back wall reflections. The size of an indication is finally quantified by reporting the diameter
or area of an equivalent artificial reflector. By comparing the noise level with the reflectivity
of equivalent defect sizes, this also allows to measure the achieved sensitivity during a
particular inspection, reported as a minimum detectable defect size. Nowadays sensitivities
are typically equivalent to ~0.7 2 mm diameter disc shaped reflectors, depending on the
size of the inspected part and the component material.
Fig. 1: Ultrasonic examination of a heavy rotor forging in 1953 [4] (left)
and automated inspection system from 1995 at Saarschmiede [2] (right).
2. Automated Data Recording
Around 1995 automated inspection systems (see Fig. 1) became available allowing a
more precise control of key factors of the ultrasonic inspection. Moreover data recording,
enhanced data processing and off-site data-review became possible.
Typically, when using automated ultrasonic inspection systems, the component is
rotated continuously (scan direction) and the probe holder is indexed along the radial or axial
axis (index direction). Due to a certain pulse repetition rate the data is recorded in a certain
grid – also called the scanning grid [5, 6]. At each point of the grid the time signal (reflected
amplitude over time) is recorded. The inspection data can then be displayed as A-Scans (x-
axis: sound propagation direction, y-axis: Amplitude), B-Scans (one axis: scan or index
direction; other axis: sound propagation direction; color coding: amplitude) and C-Scans (one
axis: scan direction; other axis: index direction; color coding: amplitude).
However, the time signal does not only contain the information from the center beam
(region “below” the probe), but is an integrated value across the beam profile of the probe
(see Fig. 2). This means that at each probe location we have accurate information about the
distance between indication and probe, but not about the direction.
Fig. 2: Beam profile of a normal probe (left)
and of a narrow beam probe (right).
On the other hand, indications are typically not only showing in the signal from one
probe location, but in the signals from multiple adjacent probe locations. As in B-Scans the
indications are plotted along the main beam axis this results in a typical hyperbola shape of
indications (see Fig 3).
The achieved sensitivity is limited both by the sound attenuation and by noise. Noise
consists of stochastic noise (e.g. due to the electrical noise of the UT flaw detector or
electromagnetically induced spikes from machines nearby) as well as echo signals caused by
the grain structure of the component material. Those grain noise signals however are
integrated over the beam profile which means that a wider beam creates a higher grain noise
level (see Fig. 2 – dark gray area).
Both facts (noise level and hyperbola shape of indications) are good arguments for
focusing the sound beam either by using larger probe sizes [7] or by using higher probe
frequencies. Higher probe frequencies will, however, lead to higher sound attenuation and
increased noise and hence reduce the inspection sensitivity. Larger probes require a more
sophisticated probe design and are more difficult to couple properly. Furthermore, they
increase the required inspection time by one order of magnitude if performed according to
standards [8] (instead of 3 angles to cover a 21° zone (7°, 14°, 21°) a much higher number of
angles and thus scans are necessary).
A more favorable option is synthetic aperture focusing realized by computer based
postprocessing of the recorded UT data. This will be shown in the following.
Fig. 3: One indication (big black dot) is found by 7 probe locations, for each probe location the distance is
known but not the angle (left); in typical B-Scans indications are plotted at the location of the probe using the
known distance; this leads to crescent shaped indications (middle); B-Scan of a real indication (right).
3. Synthetic Aperture Focusing
The knowledge how the hyperbola shaped indications are created can be used to derive
a simple heuristic method to reconstruct the real indication location. A straight forward way
would be to draw half circles at the beam exit points of the probes using the distance to the
indication as radius. These circles will intersect at the location of the indication as shown by
Fig. 3.
Mathematically a different approach is superior. The volume of the component is
divided into voxels (a 3-dimensional grid with a grid size one order of magnitude smaller
than the wavelength) and for each voxel with the coordinates 𝑟=𝑥,𝑦,𝑧 all signals are
considered which could have its origin in that voxel (𝑟
!𝑆!"). All those signals 𝑎𝑟
!,𝑡,
with probe location 𝑟
!, time 𝑡=!
!
𝑟
!𝑟, and sound velocity 𝑐, are added for each voxel
(best is to use the non-rectified high-frequency signals). This will lead to constructive
interference (synthetic aperture focusing) at the location of indications and to destructive
interference in the surrounding area (see Fig. 4) [9]:
𝐼𝑟=
𝑥
𝑦
𝑧
=𝑎𝑟
!,𝑡=
2
𝑐𝑟
!𝑟
!!!!"
.
(1)
Fig. 4: Constructive (left) and destructive (right) interference.
This means for every voxel within a 3D volume a two-dimensional summation of all
signals from the scan surface has to be conducted. This approach is called 3D-SAFT [10]. To
reduce calculation time a different approach can be taken by separating the complete 3D
volume into individual 2D slices. This reduces the computational effort to a situation that for
every “voxel” within the 2D slice a 1-Dimensional summation of the signals from one single
scan line has to be conducted [10], but with a reduced signal to noise ratio and no resolution
improvement in the direction of the “omitted” axis. The result of this 2D approach can still be
displayed in a 3D volume and by other authors is often referred to as a 2.5D imaging.
The result of both reconstruction methods is one amplitude value for each voxel, just
like in X-Ray Computed Tomography results. This is why SAFT is also called Ultrasonic
Computed Tomography.
The Synthetic Aperture Focusing Technique (SAFT) has its origin in the Synthetic
Aperture Radar (SAR) from 1967 [11]. The first implementation by D.W. Prine in 1972 [12]
was using optical components. The first digital system for NDT was realized by J.R.
Frederick in 1976 [13]. Despite the SAFT method being known for long time it required the
progress of computer technology and the advent graphics board usable for general-purpose
calculations until it could be applied for large component inspection. In 2010 Siemens and
BAM implemented SAFT for the inspection of large rotor forgings [14, 15].
Fig. 5 demonstrates the improvement of both the imaging of indications and the
sensitivity (shown by the blue noise in the classical result).
Fig. 5: Classical result of the ultrasonic inspection (left)
of a rotor forging with an outside diameter of 1460 mm
in comparison to the SAFT reconstruction (right).
4. Benefits of SAFT
The most important benefit of the presented method is the significant improvement of
the signal to noise ratio (SNR) (see Fig. 5). Both mentioned sources of noise, stochastic noise
and noise caused by grain structure can be effectively reduced. Stochastic noise is reduced by
a factor of 𝑛 , with 𝑛 different probe locations building the reconstruction result, as SAFT
can be considered an intelligent averaging method with a phase-corrected superposition of
the signals. Grain noise is reduced due to the focusing effect of SAFT (as discussed in
paragraph 2).
A second, extremely important benefit is the improvement of the lateral sizing and
resolution (see Fig. 5). Due to the focusing effect of SAFT a lateral resolution 𝐹𝑊𝐻𝑀!"# of
half the probe diameter 𝐷! can be reached [16, 17]:
𝐹𝑊𝐻𝑀!"# =
𝐷!
2.
(2)
In classical ultrasonic inspections, this resolution is only possible at the focal point of the
beam and it will even worsen with increasing metal travel path due to the increase in beam
diameter. Typical metal travel paths in large forgings (1000mm) result in very large beam
diameters (130mm) for classical standard probes.
Due to the cylinder geometry, the lateral resolution is improved further in radial scans for
locations closer to the center. For a disk without inner bore the best resolution (a quarter of
the wavelength 𝜆) is reached in the center:
𝐹𝑊𝐻𝑀!"# =
𝜆
4.
(3)
As shown in Fig. 6 the improvement of the lateral resolution also helps resolving group
indications.
The improvements in SNR in combination with the improved lateral resolution will
significantly reduce the false call rate in case of grouped indications detected on long metal
travel paths. At the same time, the determination of the indication location is simplified.
Conventionally, the determination of the indication location is challenging (in particular for
angle beam inspections) as only the distance to the indication is known and not the angle.
SAFT automatically displays the indications at their correct location.
Fig. 6: Conventional result of the ultrasonic inspection of two reflectors in close proximity (left)
in comparison to the SAFT reconstruction (right).
SAFT is easy to perform: existing automated inspection systems can be used and the
imaging of the results is similar to the imaging of the classical ultrasonic data. A-Scan, B-
Scan and C-Scan like views of the results are possible. Moreover, SAFT can be used both for
longitudinal waves and shear waves.
Finally, during classical inspections, the classification, evaluation, and localization of
indications might require additional (manual) scans to establish a reliable result. Due to the
improved determination of indication location and lateral sizing by SAFT those additional
scans can be reduced.
5. Benefits of the Presented SAFT Implementation
The presented SAFT implementation is developed for production use in the forging
industry [18, 19]. This brings certain boundary conditions (which are also applicable for any
implementation for any other industrial use). The software must be easy to use. This enables
inspectors in the forging shops to perform the reconstruction reliably and to review the data
similarly to classical UT data. The reconstruction process has to be validated and must be
faster than the actual inspection. This allows to trust the inspection results and to finish one
reconstruction while collecting the data. The aim is to keep the time delay between the last
finished scan and the review as short as possible, to finish the review of one part, before the
next one is loaded on the machine. Finally, the file sizes must be manageable.
All those goals are achieved: the results are within ±2 𝑑𝐵, the reconstruction time is,
even for 3D SAFT, below half the data acquisition time (by switching from CPU to GPU
reconstruction a speed-up by a factor of ~2000 was accomplished), and, due to combined
data compression algorithms, all necessary data is maintained.
Usually indications in the SAFT results show oscillations (see Fig. 7). Instead of using
the measured echo signals directly for SAFT reconstruction, it is possible to convert them
into complex numbered echo signals with same amplitude and phase (analytical signal) by
using the Hilbert Transformation:
𝑎𝑟
!,𝑡=𝑎𝑟
!,𝑡+𝑖𝑎𝑟
!,𝑡.
(4)
By performing the SAFT reconstruction on the complex numbered echo signals and
stripping the signal phase afterwards the oscillations are eliminated and the signal envelope is
displayed. This leads to a reconstruction result which is easier to interpret in particular as the
maximum amplitude is easier to determine. Moreover, the scanning grid can be coarser which
reduces the inspection time.
Fig. 7: SAFT result after reconstruction using real numbers (left)
and SAFT result after reconstruction using complex numbers (right).
6. SAFT: A Quantitative Technique
SAFT indications larger than the lateral resolution 𝐹𝑊𝐻𝑀!"# (which is still smaller
than the beam profile) can be sized by imaging tools. This leaves the challenge of measuring
the sensitivity of SAFT and to size small indications. For years, SAFT was considered just as
an imaging tool and up to the moment the improvement of the signal-to-noise ratio discussed
in chapter 4 could not be used to improve the inspection.
However, just like it is done in classical ultrasonics the amplitude of the SAFT signal
can also be used to gain size information [20, 21]. This is possible by comparing the
amplitude sum of the SAFT reconstruction with the amplitude sum of a reconstructed
simulation of artificial reflectors. Therefore, this method is like the DGS method just that
the SAFT-DGS table needs to be calculated for a certain component geometry.
As shown in Fig. 8 the SAFT implementation presented in this paper includes a SAFT-
DGS assessment meaning the amplitude of each voxel represents the equivalent reflectivity
of a disc shaped reflector (DSR). This makes the determination of the achieved sensitivity
and of the indication size straight forward and due to the its capability of small defect sizing
SAFT grows from an imaging tool to a full-fledged quantitative measurement technique. This
also allows quantifying the improvement of the signal-to-noise ratio.
Fig. 8: SAFT-DGS assessed SAFT result [21].
8. Summary
The first production inspections using SAFT show a sensitivity improvement of up to
one order of magnitude compared to classical ultrasonic inspections. In the centre of the
forging, which is usually one of the most critical areas from a fracture mechanics viewpoint,
the largest sensitivity improvement can be achieved.
Combined with the better resolution / spatial separation of defects (which simplifies
indication classification) and fast reconstruction times SAFT has proven to be a very reliable
and versatile addition to automated inspection systems and a game changer in ultrasonic
testing.
References
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DSR$0$!1!mm
DSR$0.98!mm
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“Anwendung von SAFT im Energiemaschinenbau”, Seminar des DGZfP Fachausschuss
Ultraschallprüfung, Berlin (2013)
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[20] R. Boehm, K. Fendt, W. Heinrich, H. Mooshofer, “Verfahren und Vorrichtung zur
Defektgrößenbewertung”, Patent DE102013211616 (2014)
[21] H. Mooshofer, R. Boehm, W. Heinrich, K. Fendt, M. Goldammer, K. Kolk, J. Vrana,
“Amplitudenbasierte Fehlergrößenbewertung mit SAFT: Auf dem Weg von der bildlichen
Darstellung zum Messverfahren”, DGZfP Jahrestagung, Koblenz (2017), Di.1.C.3
... Abb. 3: Schematische Darstellung eines Schallbündels [9] ZfP-Zeitung 169 • April 2020 Das Signal enthält nicht nur die Information des Zentralstrahls, sondern ist zudem ein integraler Wert über das Schallbündel (siehe Abbildung 3). Das bedeutet, dass an jeder Prüfkopfposition ein hoher Informationsgehalt über den Schallweg zu einer Anzeige vorliegt, aber nicht über die Richtung bzw. ...
... Das Wissen über die Entstehung der hyperbolischen Form von Anzeigen bei der klassischen Prüfung kann für die Herleitung eines einfachen heuristischen Ansatzes zur Rekonstruktion der realen Anzeigenposition verwendet werden. Wenn man an jedem Schallaustrittspunkt Halbkreise mit einem Radius entsprechend dem jeweiligen Schallweg zur Anzeige zeichnet, dann schneiden sich die Halbkreise alle am Ort der Anzeige, wie in Abbildung 4 (links) gezeigt [9,10]. ...
... Das Bauteilvolumen wird in kleine 3D-Volumenelemente (Voxel) aufgeteilt und für jedes Voxel werden alle Signale addiert, die aus diesem Voxel stammen könnten. Dies führt zu einer konstruktiven Interferenz am Ort von Reflektoren und zu destruktiver Interferenz im restlichen Volumen (siehe Abbildung 5) [9,10]. Beim Vergleich der realen Anzeige in Abbildung 4 rechts (klassisch) mit Abbildung 5 rechts (SAFT) fällt neben der Verbesserung der Abbildung der Anzeige auch das reduzierte Rauschen im Hintergrund auf. ...
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Conference Paper
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Several decades ago the first ultrasonic inspections were introduced to assure component integrity. Those were, in the beginning, manual, straight beam, contact probe inspections with simple, nondescript reporting requirements. The development of ultrasonic inspection capabilities, the change in design engineer requirements, improvements of fracture mechanics calculations, experience with operation, experience with the inspection technology, and probability of detection (PoD) drove the changes that have resulted in the current day inspections. This process is described on the example of heavy rotor forgings for land-based power generation turbines and generators and shows how sizing technologies were implemented, detection limits lowered, angle and pitch/catch (dual crystal) probes introduced, and automated systems required for the inspection. Due to all these changes, model based sizing techniques and modern ultrasonic techniques, like phased array, are being introduced globally. This paper describes the evolution of the ultrasonic inspection over the last decades and presents an outlook for tomorrow.
Conference Paper
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Heavy rotor forgings, in particular for the power generation market, are highly stressed components and the ultrasonic inspection is the most important method to guarantee a sufficient material quality throughout the volume. This is why more and more heavy rotor forgings have to be inspected using automated inspection systems guarantying a high probability of detection for possible flaws, good documentation as well as highly repeatable inspection. In contrast to manual inspection, automated inspection does not allow for an optimization of a flaw reflection by moving the probe, as the probe is continuously moved over the part surface in distinct scan lines, resulting in a distinct pattern of inspection points. To ensure full volume coverage using overlapping ultrasonic beams from neighboring inspection points, a precise definition of an examination grid is required. To assure that all critical errors are detected, multiple scan directions have to be applied as per VGB-R 504 M [1] to inspect the complete volume, resulting in a high inspection duration. Moreover most of the rotor forgings have a low sound attenuation, resulting in low pulse repetition rates and even longer inspection times. An ideal inspection grid will therefore make sure the full forging volume is covered by the inspection and reduce the inspection duration to a necessary minimum at the same time. Several standards currently specify an examination grid for manual inspection, which are not simply transferrable to automated inspection. This paper presents a solution to this problem, developed by the subcommittee “Automated UT” of the national German society for NDE (DGZfP).
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Im Energiemaschinenbau ist die Ultraschallprüfung ein unverzichtbares Werkzeug für die zerstörungsfreie Prüfung von Bauteilen, die im Betrieb hohen Belastungen unterliegen. Bei der Herstellungsprüfung handelt es sich meist um Scheiben und Wellen, die ihren Einsatz in Turbinen bzw. Generatoren finden. Der Einsatz der Synthetic Aperture Focussing Technique (SAFT) bietet hierfür mehrere Vorteile. Neben der genaueren Defektlokalisation und der besseren Trennung benachbarter Defektanzeigen ist auch die Verbesserung des gefügebedingten Signal/Rausch-Verhältnisses (SNR) ein wichtiger Grund für den Einsatz von SAFT. Im Rahmen dieses Beitrages wird auf den Einsatz von SAFT bei zylindrischen Prüflingen besonders eingegangen. Neben der Gegenüberstellung von 2D-SAFT und 3DSAFT, liegt das Hauptaugenmerk auf der mit SAFT erreichbaren Auflösung bzw. räumlichen Defekttrennung. Es wird gezeigt, wie die Auflösung mittels Simulation bestimmt werden kann, und wie sich dies im Falle einer zylindrischen Scheibe mit einer empirisch ermittelten Formel vergleicht. Für ein konkretes Beispiel wird dargestellt wie sich die Auflösung in Abhängigkeit des verwendeten Prüfkopfes mit zunehmender Tiefenlage verbessert.
Article
Full-text available
Heavy rotor forgings for land-based power generation turbines and generators are inspected ultrasonically. Several decades ago the first inspections were conducted using manual, straight beam, contact transducers with simple, non-descript reporting requirements. The development of ultrasonic inspection capabilities, the change in design engineer requirements, improvements of fracture mechanics calculations, experience with turbine operation, experience with the inspection technology, and probability of detection drove the changes that have resulted in the current day inspection requirements: sizing technologies were implemented, detection limits were lowered, angle and pitch/catch (dual crystal) scans were introduced, and most recently automated equipment for the inspection was required. Due to all these changes, model based sizing techniques, like DGS, and modern ultrasonic techniques, like phased array, are being introduced globally. This paper describes the evolution of the ultrasonic inspection requirements over the last decades and presents an outlook for tomorrow.
Article
Full-text available
All types of heavy forgings that are used in energy machine industry, rotor shafts as well as discs, retaining rings or tie bolts are subject to extensive nondestructive inspections before they are delivered to the customer. Due to the availability of the parts in simple shapes, these forgings are very well suited for full volmetric inspections using ultrasound. In the beginning, these inspections were carried out manually, using straight beam probes and analogue equipment. Higher requirements in reliability, efficiency, safety and power output in the machines have lead to higher requirements for the ultrasonic inspection in the form of more scanning directions, higher sensitivity demands and improved documentation means. This and the increasing use of high alloy materials for ever growing parts, increase the need for more and more sophisticated methods for testing the forgings. Angle scans and sizing technologies like DGS have been implemented, and for more than 15 years now, mechanized and automated inspections have gained importance since they allow better documentation as well as easier evaluation of the recorded data using different views (B- C- or D-Scans), projections or tomography views. The latest major development has been the availability of phased array probes to increase the flexibility of the inspection systems. Many results of the ongoing research in ultrasonic's have not been implemented yet. Today's availability of fast computers, large and fast data storages allows saving RF inspection data and applying sophisticated signal processing methods. For example linear diffraction tomography methods like SAFT offer tools for D reconstruction of inspection data, simplifying sizing and locating of defects as well as for improving signal to noise ratios. While such methods are already applied in medical ultrasonic's, they are still to be implemented in the steel industry. This paper describes the development of the ultrasonic inspection of heavy forgings from the beginning up to today at the example of Saarschmiede GmbH explains the difficulties in implementing changes and gives an outlook over the current progression.
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One way of achieving fine-resolution terrain imagery using airborne, side-looking radar is to boost frequency; another is to decrease along-track tracking. Neither is attractive. But they would have had to do were it not for coherent wave radar¿upon which synthetic-aperture radar is premised. Using coherent radar, resolution can depend, not on the width of the beam, but on Doppler frequency shift. The azimuthal resolution of side-looking radar can therefore be of the same order of magnitude as that for range resolution. The key to converting the theoretical groundwork into a ``full-bodied'' system is an appropriate data-processing scheme. And the simplest scheme for working, processing, and deciphering the data is optical.
Article
The general theory of side-looking synthetic aperture radar systems is developed. A simple circuit-theory model is developed; the geometry of the system determines the nature of the prefilter and the receiver (or processor) is the postfilter. The complex distributed reflectivity density appears as the input, and receiver noise is first considered as the interference which limits performance. Analysis and optimization are carried out for three performance criteria (resolution, signal-to-noise ratio, and least squares estimation of the target field). The optimum synthetic aperture length is derived in terms of the noise level and average transmitted power. Range-Doppler ambiguity limitations and optical processing are discussed briefly. The synthetic aperture concept for rotating target fields is described. It is observed that, for a physical aperture, a side-looking radar, and a rotating target field, the azimuth resolution is ¿/¿ where ¿ is the change in aspect angle over which the target field is viewed, The effects of phase errors on azimuth resolution are derived in terms of the power density spectrum of the derivative of the phase errors and the performance in the absence of phase errors.
Erfahrungen mit der Ultraschallprüfung bei der Abnahme von Rotoren für Turbosätze
  • R Schinn
R. Schinn, "Erfahrungen mit der Ultraschallprüfung bei der Abnahme von Rotoren für Turbosätze", Metall (1953, 7), pp. 502-506
Guideline for the determination of the scanning grid for the automated ultrasonic testing of large forgings
  • Dgzfp
DGZfP, "Guideline for the determination of the scanning grid for the automated ultrasonic testing of large forgings", DGZfP, Berlin (2017)
Improved Inspection Technique for Large Rotor Shafts, Using a Semi-Flexible Phased Array Probe
  • G Maes
  • P Tremblay
  • D Devos
  • N Hoshi
  • H Nimura
  • H Narigasawa
G. Maes, P. Tremblay, D. Devos, N. Hoshi, H. Nimura, H. Narigasawa, "Improved Inspection Technique for Large Rotor Shafts, Using a Semi-Flexible Phased Array Probe", Int. Conf. on NDE in Relation to Structural Integrity for Nuclear and Pressurized Components, Jeju (2015, 11)