high-speed digital scan converter for high-frequency ultrasound sector scanners

Available online at www.sciencedirect.com

www.elsevier.com/locate/ultras

Ultrasonics 48 (2008) 444–452

High-speed digital scan converter for high-frequency ultrasoundsector scanners

Jin Ho Chang *, Jesse T. Yen, K. Kirk Shung

NIH Resource Center for Medical Ultrasonic Transducer Technology, Department of Biomedical Engineering,

University of Southern California, Los Angeles, CA 90089, United States

Received 18 October 2007; received in revised form 3 March 2008; accepted 6 March 2008Available online 14 March 2008

Abstract

This paper presents a high-speed digital scan converter (DSC) capable of providing more than 400 images per second, which is nec-essary to examine the activities of the mouse heart whose rate is 5–10 beats per second. To achieve the desired high-speed performance incost-effective manner, the DSC developed adopts a linear interpolation algorithm in which two nearest samples to each object pixel of amonitor are selected and only angular interpolation is performed. Through computer simulation with the Field II program, its accuracywas investigated by comparing it to that of bilinear interpolation known as the best algorithm in terms of accuracy and processing speed.The simulation results show that the linear interpolation algorithm is capable of providing an acceptable image quality, which means thatthe difference of the root mean square error (RMSE) values of the linear and bilinear interpolation algorithms is below 1%, if the samplerate of the envelope samples is at least four times higher than the Nyquist rate for the baseband component of echo signals. The designedDSC was implemented with a single FPGA (Stratix EP1S60F1020C6, Altera Corporation, San Jose, CA) on a DSC board that is a partof a high-speed ultrasound imaging system developed. The temporal and spatial resolutions of the implemented DSC were evaluated byexamining its maximum processing time with a time stamp indicating when an image is completely formed and wire phantom testing,respectively. The experimental results show that the implemented DSC is capable of providing images at the rate of 400 images per sec-ond with negligible processing error.� 2008 Elsevier B.V. All rights reserved.

Keywords: Digital scan conversion; Linear interpolation; High frame rate; Ultrasound sector scanner; High-frequency ultrasound imaging

1. Introduction

High frequency ultrasound transducers have made itpossible to open up new applications including ophthalmic,dermatologic, intravascular, small animal, and molecularimaging [1–4] because of their fine spatial resolution onthe order of several tens of micrometers. Among theseapplications, especially, the cardiac imaging of a mouserequires a fine temporal resolution as well. This is sobecause the heart rate of a mouse is 5–10 beats per secondand thus the frame rate should be at least on the order of150–300 per second or more in order to adequately exam-

0041-624X/$ - see front matter � 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.ultras.2008.03.001

* Corresponding author. Tel.: +1 213 740 0520; fax: +1 213 821 3897.E-mail address: [email protected] (J.H. Chang).

ine the activities of the mouse heart such as valve move-ment [5,6]. For the purpose of the mouse heart imaging,therefore, high-speed data acquisition is a pivotal elementand it can be realized by using array transducers with elec-tronic translation. Xu et al. reported an analog beamform-ing system for 35-MHz linear arrays, which is capable ofproducing images at up to 100 frames per second [4].And they claimed that the system can provide much fasterframe rate than the current one if microcontroller speedand data transfer rate from the beamformer to a personalcomputer (PC) are improved. However, the width ofimages produced in the system with the linear array trans-ducer is too narrow to efficiently examine mouse heartactivities. High frequency convex arrays could be a possiblesolution to the problem because its fabrication is relativelyeasy compared to phased arrays that requires a fine pitch of

mailto:[email protected]

Fig. 1. Conceptual representation of bilinear and linear interpolation.

J.H. Chang et al. / Ultrasonics 48 (2008) 444–452 445

less than a half wavelength in order to remove grating lobeartifacts. Kim et al. proposed a design of 20-MHz convexarrays for ophthalmic imaging to increase the field of viewin azimuthal direction and stressed that the center fre-quency of the convex arrays can be increased to around40 MHz which is the limitation in the current array fabrica-tion technology [7]. Once the convex arrays are available, itmight be the best tool examining mouse heart activities.Without these arrays, however, a high-speed mechanicalsector scanner with a single element transducer can be usedas an interim tool for the examination of mouse cardiacactivities, which is currently capable of providing a framerate of up to 130 frames per second with a view angle of22� [8].

Besides the high-speed data acquisition, it is anotherchallenge to develop high-speed signal processing functionsto support high frame rate imaging of more than 300frames per second. This is so because these functions mustbe capable of providing very fast computational speed andwide bandwidth of data transfer between each functionalblock. Among the functions, the development of a high-speed digital scan converter (DSC) is crucial to map theacquired echo samples onto the pixels of a monitor becauselocation mismatch between the samples and the pixels isespecially serious in the sector scanning.

The simplest way to map echo samples onto pixels is toassign echo samples to the nearest pixels [9]. However, theecho samples are typically more abundant in the axialdirection but less in the lateral direction. When the samplesare mapped onto pixels, pixels located in between two scan-lines may not be assigned with any samples, causing theMoire artifact [9]. This phenomenon is obvious in sectorscanning because pixels located far from a transducer havea less possibility to be assigned with a sample. In sectorscanning, therefore, the scan conversion mainly involvesdata interpolation requiring coordinate transformation ofa pixel from Cartesian coordinates to polar coordinatesor vice versa. Various data interpolation algorithms wereproposed, and their performances were examined [10–15].Among these algorithms, bilinear interpolation is knownas the best algorithm in terms of accuracy and processingspeed. However, hardware implementation of this algo-rithm may be very costly because the bilinear interpolationinvolves complex operations such as square root and arc-tangent computations in order to convert pixel positionsin a Cartesian coordinate into a polar coordinate, and viceversa [12]. In addition, the interpolation algorithm involvesat least four data-fetch operations that require complicatedbuffer management logic circuits. This high cost for theimplementation of the bilinear interpolation is particularlytrue when the operating speed of DSC is pushed higher andhigher because electronic components become more expen-sive and more sophisticated design is required to meet itstiming constraints.

This paper reports a recently developed high-speed DSCthat is capable of providing high-frequency B-mode imagesat a rate of up to 400 images per second of which an image

size is 256 by 256 pixels. For the sake of simple implemen-tation, this DSC employs a linear interpolation algorithmthat is a simplified version of the bilinear interpolationalgorithm, thus allowing a high-speed operation in simpleand cost effective manner. In the paper, the accuracy ofthe linear interpolation is examined with the Field II simu-lation program [16], and it is shown that the linear interpo-lation algorithm is capable of providing comparable imagequality to the bilinear interpolation if a sampling rate ofenvelope samples is at least four times higher than theNyquist rate for the baseband component of echo signals.Experimental results, in addition, verify that the DSCdeveloped provides satisfactory performance for high-speed, high-frequency ultrasound imaging.

2. Linear interpolation

Bilinear interpolation algorithm is two-dimensionalinterpolation: the first order Lagrange interpolation [17],called linear interpolation, along radial and angular direc-tions. Therefore, the value of a pixel P in Fig. 1 can beobtained by the following calculations:

I i ¼ S1�R2þS3�R1

R1þR2;

I iþ1 ¼ S2�R2þS4�R1

R1þR2;

ð1Þ

AP ¼I i � aþ I iþ1 � b

aþ b; ð2Þ

where S1–S4 are the values of samples surrounding the ob-ject pixel P, a and b are angular differences between P andtwo scanlines SLi and SLi+1, and R1 and R2 are radial dif-ferences between P and two samples located on SLi andSLi+1, respectively. Ii and Ii+1 are intermediate values ontwo scanlines SLi and SLi+1, respectively.

Linear interpolation is a simplified version of the bilin-ear interpolation. Unlike the bilinear interpolation, linearinterpolation involves only an angular interpolation givenby

446 J.H. Chang et al. / Ultrasonics 48 (2008) 444–452

AP ¼S1 � aþ S2 � b

aþ b; ð3Þ

where S1 and S2 are selected because they are the nearestsamples to P along radial direction. Although linear inter-polation is easily implemented and reduces the complexityof buffer management logic to fetch stored samples for datainterpolation, its accuracy is inferior to bilinear interpola-tion if the sampling rate in the radial direction is low. Ifthe sample rate along radial direction, i.e., of envelope datais increased, the accuracy of linear interpolation would beimproved. Richard and Arthur [13] verified this fact withvarious B-mode images that if being performed with enve-lope data over-sampled by a factor of 2 or more, linearinterpolation can provide superior image quality to bilinearinterpolation with the original data that are sampled tomatch pixel-to-pixel spacing. This result sheds light onthe relationship between the number of samples along ra-dial direction and the improvement of the accuracy of lin-ear interpolation. It, however, does not yield any clues as tothe relative accuracy of these two algorithms because theaccuracy of the bilinear interpolation can be improved withthe over-sampled envelope data as well. Intuitively, bilinearinterpolation would have superior or equal accuracy to thelinear interpolation if the same number of envelope sam-ples is involved in each processing. In order to determinea suitable sampling rate that makes linear interpolationprovide an acceptable image quality, it is necessary toquantitatively compare the accuracy of linear and bilinearinterpolation in the situation where the same number ofenvelope samples is used for the processing.

A comparison of accuracy of these two algorithms wasundertaken by using the Field II simulation program [16].In the simulation, a 40-MHz single element transducermodel was used. Its focal depth was 8 mm, F-numberwas 2.5, and the spectrum had a bandwidth of 40 MHz.Five targets, 1.4 mm apart in the lateral direction along adepth of 8 mm, were scanned by means of the mechanicalsector scanning in which the viewing angle was 50� and181 number of scanlines were obtained. Echo signals wereacquired at a sampling rate of 800 MHz and Hilbert trans-formation was carried out to extract the exact envelope

Table 1Comparison of accuracy of linear and bilinear interpolations by computerevaluated with the normalized RMSE between pixel values obtained by each

fs 2fmax (%) 4fmax (%) 5f

Algorithm The normalized RMSE

(a) A pixel-to-pixel space of 2fmax

Bilinear interpolation 8.56 7.40 7.Linear interpolation 12.19 9.46 9.Differences 3.63 2.06 1.

(b) A pixel-to-pixel space of 4fmax

Bilinear interpolation 8.77 7.08 6.Linear interpolation 12.79 9.21 8.Differences 4.02 2.13 2.

In this table, fs is a sampling frequency and fmax is the highest frequency of b

information from the echo signals. After the ideal envelopedetection, the information was logarithmically compressedto a 72 dB dynamic range so that it can be used for eachinterpolation algorithm.

Once the locations of pixels are transformed from aCartesian coordinate to a polar coordinate, each pixelhas a unique angle and radius. In order to obtain a pixelvalue without the error caused by both radial and angularinterpolations, a transducer can be rotated by the angle ofa pixel in a polar coordinate and an envelope sample cor-responding to the radius of the pixel among the samplesgenerated at an extremely high sampling rate like 2 GHzcan be selected. By repeating the procedure for the entirenumber of pixels, we can obtain an error-free image. Inthe simulation, a standard image used for the comparisonwas created by this manner.

In common ultrasound imaging systems, baseband echosamples obtained by quadrature demodulation are deci-mated along with the bandwidth of the samples. This ispossible because the sampling rate of the systems for digi-tizing radio-frequency echo signals is much higher than thebandwidth of their baseband counterpart. Decimation canbe increased until the new sampling rate satisfies theNyquist rate for the baseband signals. By doing so, thesquare root function used to obtain envelope informationfrom the baseband complex signals is given enough timeto compute the envelope data and a small amount of mem-ory is needed to store the results. For displaying images ona monitor, the space between two adjacent pixels is alsodetermined so that it can satisfy the Nyquist rate for theenvelope signals to avoid the Moire artifact once an imagedepth for displaying is chosen. As a result, the simulationwas performed with the two pixel-to-pixel spaces of37 lm and 18.5 lm corresponding to one and two timesthe Nyquist rate for the baseband signals, respectively.DSC with linear and bilinear interpolations was performedwith various factors of decimation, i.e., various samplingrates under the each pixel-to-pixel space. The accuracy ofeach interpolation algorithm along with a sampling ratewas evaluated by computing the normalized root meansquare error (RMSE) between pixel values obtained by

simulation using Field II program; the accuracy of each algorithm wasinterpolation algorithm and exact pixel values

max (%) 8fmax (%) 10fmax (%) 20fmax (%)

30 7.21 7.13 7.1200 7.86 7.72 7.4070 0.65 0.59 0.28

68 6.38 6.36 6.2889 7.12 6.63 6.5521 0.74 0.27 0.27

aseband echo signals of 20 MHz in the simulation.

Fig. 3. Lateral beam profiles of three point targets shown in Fig. 2. Toppanel is for a point target at 0 mm in lateral direction and 8 mm in axialdirection, middle panel is for it at �1.4 mm and 8 mm, and bottom panelis for it at �2.8 mm and 8 mm.


the each algorithm and exact pixel values. Table 1 showsthe normalized RMSE values along with each pixel-to-pixel space.

As indicated above, Table 1 shows that bilinear interpo-lation is always capable of providing the superior accuracyto linear interpolation even though sampling rate increases.However, the differences between the accuracy of these twoalgorithms decrease with sampling rate and become below1% as the sampling rate approaches to 8fmax that is fourtimes higher than the Nyquist rate for the baseband com-ponent of the echo signals. The symbol fmax is the highestfrequency component of the bandwidth of the basebandecho signals. With a high sampling rate, therefore, linearinterpolation is capable of providing similar image qualityas bilinear interpolation.

Fig. 2 shows point target images with a 72 dB dynamicrange obtained by the Field II simulation when the sam-pling rate is 40 MHz (2fmax) and the pixel-to-pixel spaceis 18.5 lm. The images in top, middle, and bottom panelswere respectively obtained by the exact solution, DSC withbilinear interpolation, and DSC with linear interpolation.This figure shows that the error from linear interpolationmakes the image of the point targets, located in �2.8 mmand �1.4 mm, more blocky whereas bilinear counterpartmakes it more blurry. However, the point target imagelocated in the center scanline, i.e., 0 mm in the lateral direc-tion shows almost similar quality in both cases. As a result,it appears that interpolation error more affects the image oftargets located away from the center scanline than these invicinity of the center scanline. This is easily seen fromFig. 3 illustrating lateral beam profiles of the three pointtargets located at 0 mm (top panel), �1.4 mm (middlepanel), and �2.8 mm (bottom panel). The error imposed

Fig. 2. Point target images obtained when a sampling rate is 40 MHz(2fmax) and the pixel-to-pixel space is 18.5 lm. The images in top, middle,and bottom panels were obtained by the exact solution, DSC with bilinearinterpolation, and DSC with linear interpolation, respectively.

on the lateral beam profile in the top panel appears to berestricted to below �60 dB level for both linear and bilinearinterpolations, whereas in the middle and bottom panels itappears that the error exists for the entire profile in bothcases. In the case of linear interpolation, especially, theoff-center lateral beam profiles look like stairs due to thelack of envelope samples, which make the image appearblocky. However, this problem is alleviated as the samplingrate increases as illustrated in Figs. 4 and 5 which showpoint target images obtained with a sampling rate of100 MHz (5fmax) and their lateral beam profiles,respectively.

A sampling rate of 100 MHz is still considered slow forlinear interpolation to provide an acceptable image quality,meaning that the difference of the RMSE values of linearand bilinear interpolations should be below 1%. At thissampling rate, however, the image obtained with linearinterpolation (bottom panel in Fig. 4) appears to be muchsmoother than the previous one. In addition, its lateralbeam profiles shown in Fig. 5 become closer to theseobtained with bilinear interpolation.

The results suggest that in order to use linear interpola-tion to implement DSC operating at a very high speed withthe acceptable image quality, the envelope sample rateshould be at least four times higher than the Nyquist ratefor the baseband component of echo signals. This require-ment can be achieved by either radial interpolation with

Fig. 4. Point target images obtained when a sampling rate is 100 MHz(5fmax) and the pixel-to-pixel space is 18.5 lm. The images in top, middle,and bottom panels were obtained by the exact solution, DSC with bilinearinterpolation, and DSC with linear interpolation, respectively.

Fig. 5. Lateral beam profiles of three point targets shown in Fig. 4. Toppanel is for a point target at 0 mm in lateral direction and 8 mm in axialdirection, middle panel is for it at �1.4 mm and 8 mm, and bottom panelis for it at �2.8 mm and 8 mm.


decimated envelope samples [13] or a very high-speed enve-lope detector capable of generating envelope samples at thesame rate of the sampling clock of a system [18].

3. Implementation of DSC

Fig. 6 illustrates the functional block diagram of thedesigned DSC with the linear interpolation algorithm.The logarithmic compressed envelope data are sent toone of three line buffers; each line buffer is capable of stor-ing data corresponding to a scanline. Once the two line buf-fers finish storing the data, scan conversion starts for pixelswithin a sector scan slice formed by two correspondingscanlines to the line buffers while the other is storing thecurrent envelope data. The pixel address generator (PAG)provides the line buffer read address generator (LBRAG)and the fractional angle generator with the indices of pixelswithin a sector scan slice identified by a left scanline num-ber (LEFT_SL). In Fig. 7, for example, the sector scan sliceformed by scanlines SLi and SLi+1 is identified by SLi

located on the left side of the slice. In order to achievethe desired operating speed, LBRAG and the fractionalangle generator responsible for coordinate transformationare implemented by a look-up table (LUT) method thatuses the symmetry property of a sector scan image toreduce the size of LUT.

3.1. Pixel address generator

The generation of pixel addresses corresponding to agiven sector scan slice can be also realized by a LUTmethod. Each pixel belongs to only one among sector scanslices, and the number of pixels within a given sector slice isdetermined by several factors: number of scanlines, viewingangle of imaging plane, imaging depth, and number of pix-els in an image. Once these factors are determined, we candetermine which pixels belong to which sector scan slices,so that the space of LUT can be divided by the numberof the slices constituting an imaging plane and the eachspace contains the addresses of pixels within the corre-sponding slice. With LEFT_SL values indicating each slice,therefore, PAG sends the addresses of pixels within the cur-rent sector scan slice to LBRAG, the fractional angle gen-erator, and a display memory block.

However, the direct realization of the LUT methodrequires a large size of memory, i.e., (N � 1) �M �log2(Kx � Ky) bits, where N is the number of scanlines,M is the maximum number of pixels within a given sectorscan slice, and Kx � Ky is the image size. For the case of a512 by 512 image and 200 scanlines, for example, the mem-ory size should be 4.7 Mbits where M is obtained by thecalculation (512 � 512/200).

In order to reduce the memory size, the digital scan con-verter is designed to perform the function of encoding thepixel addresses. Each pixel within a given sector scan slice,called an effective pixel group, is vertically subdivided intoG0–G7 indicated by dotted rectangles in Fig. 7 as an exam-ple. Each subgroup has a leading pixel represented by dot-ted circles. It should be noted that a pixel address in asubgroup can be calculated by a leading pixel addressand the object pixel position number in the subgroup.

Fig. 6. Functional block diagram of designed digital scan converter with linear interpolation.

Fig. 7. Description of grouping pixels and linear interpolation within twoadjacent scanlines SLi and SLi+1 indicated by bold dashed lines. Amultiplication sign represents an image pixel. A dotted rectangle repre-sents one of subgroups of the pixel group within the two scanlines. Adotted circle designates a leading pixel in each subgroup. Filled circles onthe scanlines represent acquired samples. The multiplication sign in adiamond is an object pixel to linear interpolation. a and b are angulardifferences between P and SLi and SLi+1.

Fig. 8. An example to describe the contents of LUT and its output value.Left scanline number SLi and a subgroup number constitute an index ofLUT. For the sector scan slice in Fig. 7, the number of indices is eightbecause there are eight subgroups. Each entry corresponding to the indicescontains a leading pixel address and the number of a subgroup member. Incase of the second index representing subgroup G1, its entry contains theleading pixel address X1Y6 and number four. Its outputs are generated byincreasing a leading pixel address by one as many as the number of asubgroup member minus one.


For instance, the address of the object pixel P in subgroupG4 is obtained by adding its position number of 6 to the Y-axis component of the leading pixel address X4Y0, so thatthe address becomes X4Y6. Therefore, both LEFT_SL val-ues and subgroup numbers in each effective pixel group canplay the role of indices of LUT. Each entry of the LUTstanding for the indices contains a leading pixel addressand the number of a subgroup member. The memory sizefor this LUT strategy is therefore

Memory Size ðbitsÞ ¼ ðN � 1Þ � Kx

2� log2ðKx � Ky � KyÞ:

ð4ÞUnder the previous condition, the memory size for LUT isreduced from 4.7 Mbits to 1.4 Mbits. Fig. 8 shows anexample describing the contents of LUT and its output va-

lue for the sector scan slices in Fig. 7. The number of LUTindices is eight because there are eight subgroups. Each en-try corresponding to the indices contains a leading pixel ad-dress and the number of a subgroup member. For thesecond index representing subgroup G1, its entry containsthe leading pixel address X1Y6 and four that is the numberof G1 member.

3.2. Coordinate transformer and interpolator

In order to perform coordinate transformation, eachpixel constituting an image is assigned a unique addressin a Cartesian coordinate as shown in Fig. 9, which is anexample of pixel addressing of 256 by 256 sized image.Eight most significant bits correspond to a location in X-axis whereas the other bits a location in Y-axis. For exam-ple, hexadecimal 0�8000 in Fig. 9 is composed of 0�80 fora X-axis location and 0�00 for a Y-axis location. The ref-erence column indicates the center in X-axis. An interestingfeature in this addressing is that X-axis components of twodifferent pixels equally distant from the reference columnare two’s complement to each other. In Fig. 9, for example,X-axis components of 0�7F00 and 0�8100 are two’s com-

Fig. 9. Configuration of pixel addressing of 256 by 256 sized image. Thereference column indicates the center in X-axis.


plement, i.e. 0�100 � 0�7F = 0�81. By using this feature,the size of LUT for coordinate transformation can bereduced to approximately half.

A pixel address provided by PAG is sent to LBRAG andthe fractional angle generator to perform coordinate trans-formation and linear interpolation. The two functionalblocks can be straightforwardly implemented by a LUTmethod. The indices of LUTs belonging to the two func-tional blocks are the addresses of pixels located on boththe reference column and its left side in Fig. 9. The rightside pixel addresses are converted into two’s complementforms to obtain their corresponding values from the entriesfor their equal distance pixel addresses on the left of theimage plane. Entry values of the LUTs are computed inPC and loaded into the LUTs.

LBRAG plays a role in providing the line buffers withthe sample address corresponding to a given pixel addressto make the line buffers send the samples to the calculationblock. Entries of LUT in LBRAG can be calculated by

Sample Address ¼ roundDd �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðX j � X CÞ2 þ Y 2

j

qDsample

0@

1A; ð5Þ

where Xj and Yj represent a X-axis and Y-axis address com-ponents of the jth pixel and XC is a X-axis address compo-nent of reference column corresponding to origin in theCartesian coordinate. In Eq. (5), Dd is a distance betweentwo successive pixels in horizontal or vertical directions,Dsample is a sample interval, and round(�) is a function pro-ducing the nearest integer value. Note that the two samplevalues S1 and S2 in Eq. (3) are located at the same addressof two different line buffers.

The fractional angle generator has a LUT in whichentries are b values in Eq. (3). If the angle of ith scanlineis hSLi and the angular difference between SLi and SLi+1

is predetermined value Dh, b can be obtained by

b ¼ hSLi � tan�1 X j � X C

Y j

� �ð6Þ

and a can be simply calculated by

a ¼ Dh� b: ð7ÞTherefore, the fractional angle generator consists of LUTcontaining precomputed b and a subtractor to calculate a.

4. Experimental results

In order to evaluate the performances of the designedDSC, it was implemented in a single FPGA (StratixEP1S60F1020C6, Alteral Corporation, San Jose, CA) ona DSC board operating at 100 MHz that is a part of ahigh-speed ultrasound imaging system developed. Echo sig-nals are digitized by a 12-bit analog-to-digital converter(AD9430, Analog Devices Inc., Norwood, MA) at200 MHz and sent to the DSC board via a low voltage dif-ferential signaling (LVDS) bus. The DSC board contains ahigh-speed envelope detector capable of generating loga-rithmic-compressed envelope samples at a sampling rateof 200 MHz [18], so that the designed DSC involving linearinterpolation is capable of providing acceptable imagequality. In addition, the board has a 64-bit, 33-MHz PCIbus controller to transfer pixel data to a display modulein a personal computer (PC), which was implemented bysoftware programs written in C++. The display moduleis responsible for displaying images on a monitor and stor-ing the images in a hard disk of PC. At present, the displaymodule can store one thousand successive images with timestamps indicating when an image data is completely storedin PC memory. In these experiments, a mechanical sectorscanner capable of scanning at the rate of up to 130 framesper second was used [8]. The scanner mechanically trans-lates a 40-MHz light-weigh single element transducer ofwhich the focal depth is 8 mm and the F-number is 2.5 [19].

The maximum processing speed of the implementedDSC was evaluated by using four-cycle 25-MHz sinusoidalburst signals at the pulse repetition frequency (PRF) of80 kHz, which were generated by a function generator(33250A, Agilent Technologies Inc., Palo Alto, CA) andfed into the input port of the system. The system treatedthe burst signals as echo signals. Scan conversion withthe signals was performed under the condition where thenumber of scanlines was 200 and the maximum view anglewas 15�. Scan converted images were sent to the displaymodule and stored in a hard disk of PC with a time stamp.The time stamp recorded in a file showed that the maxi-mum frame rate was 400 images per second. This is anobtainable maximum rate with 100-MHz operation clockand 256 by 256 image size. On the other hand, the displayrate of the images was 95 images per second due to the lim-ited capability of a monitor. This display rate was obtainedby an experiment in which PRF was increased while dis-playing one out of two images. The maximum PRF with-out missing an image was 38.5 kHz corresponding to


about 190 images per second (38.5 � 103/200); thus themaximum display rate was one half of 190 images persecond.

The spatial resolution of the implemented DSC was eval-uated by wire phantom testing. Fig. 10 shows a wire phantomimage consisting of five 20 lm diameter tungsten wires (Cal-ifornia Fine Wire Co., CA) separated by distance intervalsalong vertical and horizontal directions of 1.5 mm and0.65 mm, respectively. The total scanlines were 108, the scan-ning angle was 12.8�, and a logarithmic compression with a60 dB dynamic range was performed. The scan conversionwas performed with 2048 samples, so that imaging depthwas 7.88 mm. Since the scan conversion started from 4 mmdepth, the maximum image depth is 11.88 mm and the thirdwire image in the vicinity of the focal depth of the transducer,8 mm, has the best spatial resolution: the�6 dB axial and lat-eral resolution of 48 lm and 103 lm, respectively.

The accuracy of these spatial resolutions was evaluatedwith the �6 dB axial and lateral resolutions computedfrom RF data which are 45 lm and 110 lm, respectively.In the case of the axial resolution, the implemented DSCdegrades it by 3 lm due to interpolation error, but the dif-ference is negligible. On the other hand, the lateral resolu-tion of the DSC is better than the one computed from RFdata by 7 lm. This can happen because the DSC performedinterpolation along the lateral direction. For the lateral res-olution, a �6 dB lateral position was determined by aver-aging two lateral positions located at right before andafter �6 dB value. After finding the other of �6 dB lateralposition in the same way, the �6 dB lateral resolution wasdetermined by computing the difference between these two

Fig. 10. Wire phantom image consisting of five 20 lm diameter tungstenwires of which distance intervals along vertical and horizontal directionare 1.5 mm and 0.65 mm, respectively.

�6 dB lateral positions. Therefore, the �6 dB lateral reso-lution of the implemented DSC can be narrower than thatcomputed with RF data when no interpolation is per-formed along the both lateral and axial directions. Fromthese results, consequently, it is seen that the system iscapable of achieving accurate results because of its negligi-ble signal processing error.

5. Conclusion

In this paper, a high-speed digital scan converter forhigh frequency ultrasound sector scanners has beendescribed. It employs a linear interpolation algorithm inwhich two nearest samples to each object image pixel areselected and an angular interpolation is performed. Sincethe linear interpolation carries out only angular interpola-tion unlike bilinear interpolation, coordinate transforma-tion providing interpolation coefficients can be simplyimplemented compared to the bilinear counterpart. Inaddition, the linear interpolation involves two data-fetchoperations instead of four in the case of the bilinear coun-terpart, which reduces the complexity of the buffer manage-ment logic. These advantages of the linear interpolationenabled us to implement a high-speed DSC in a simpleand cost effective manner. In terms of accuracy, however,it is obvious that the linear interpolation is inferior to bilin-ear one because it does not perform the interpolation alongradial direction. If the sampling rate along radial direction,i.e., the envelope sample rate is increased, the accuracy ofthe linear interpolation would be improved. Through com-puter simulation with the Field II program, therefore, ithas been shown that the linear interpolation algorithm iscapable of providing an acceptable image quality if thesampling rate of envelope samples is at least four timeshigher than the Nyquist rate for the baseband componentof echo signals.

The designed high-speed DSC was implemented in a sin-gle FPGA on a DSC board that is a part of a high-speedultrasound imaging system developed. The performancesof the implemented DSC were evaluated by experimentsin terms of temporal resolution and spatial resolution.The temporal resolution of the DSC was 400 images persecond that is applicable to cardiac imaging of the mousewhere the heart rate is 5–10 beats per second. And the spa-tial resolutions of the DSC were 48 lm and 103 lm in axialand lateral directions, respectively. These values are com-parable to those computed from RF data which are45 lm and 110 lm, respectively. As a result, the cost-effec-tive high-speed DSC with acceptable performances wouldserve as a viable alternative for examining the activitiesof the mouse heart like valve movement with high-perfor-mance high-frequency array transducers.

Acknowledgement

The support of NIH Grants Nos. R01-HL079976 andP41-EB2182 is gratefully acknowledged.


References

[1] F.S. Foster, C.J. Pavlin, G.R. Lockwood, L.K. Ryan, K.A. Hara-siewicz, L. Berube, A.M. Rauth, Principles and applications ofultrasound backscatter microscopy, IEEE Trans. Ultrason. Ferro-elect. Freq. Contr. 40 (1993) 608–616.

[2] C. Passmann, H. Ermert, A 100-MHz ultrasound imaging system fordermatologic and ophthalmologic diagnostics, IEEE Trans. Ultrason.Ferroelect. Freq. Contr. 43 (1996) 545–552.

[3] H.-D. Liang, M.J.K. Blomley, The role of ultrasound in molecularimaging, Brit. J. Radiol. 76 (2003) S140–S150.

[4] X.-C. Xu, C.-H. Hu, L. Sun, J.T. Yen, K.K. Shung, High-frequencyhigh frame rate ultrasound imaging system for small animal imagingwith linear arrays, in: Proc. IEEE Ultrason. Symp., 2005, pp. 1431–1434.

[5] F.S. Foster, G. Liu, J. Mehi, B.S. Starkoski, L. Adamson, Y. Zhou,K.A. Harasiecwicz, L. Zan, High frequency ultrasound imaging: fromman to mouse, in: Proc. IEEE Ultrason. Symp., 2000, pp. 1633–1638.

[6] E. Cherin, R. Williams, A. Needles, G. Liu, C. White, A.S. Brown,Y.-Q. Zhou, F.S. Foster, Ultrahigh frame rate retrospective ultra-sound microimaging and blood flow visualization in mice in vivo,Ultrasound Med. Biol. 32 (2006) 683–691.

[7] H.H. Kim, J.H. Chang, J.M. Cannata, K.K. Shung, Design of20 MHz convex array transducers for high frequency ophthalmicimaging, in: Proc. IEEE Ultrason. Symp., 2007, pp. 88–91.

[8] L. Sun, W.D. Richard, J.M. Cannata, C.C. Feng, J.A. Johnson, J.T.Yen, K.K. Shung, A high-frame rate high-frequency ultrasonicsystem for cardiac imaging in mice, IEEE Trans. Ultrason. Ferroelect.Freq. Contr. 54 (2007) 1648–1655.

[9] J. Ophir, N.F. Maklad, Digital scan converters in diagnosticultrasound imaging, Proc. IEEE 67 (1979) 654–664.

[10] H.G. Larsen, S.C. Leavitt, An image display algorithm for use in realtime sector scanners with digital scan converters, in: Proc. IEEEUltrason. Symp., 1980, pp. 763–765.

[11] D.E. Robinson, P.C. Knight, Interpolation scan conversion in pulse-echo ultrasound, Ultrason. Imag. 4 (1982) 297–310.

[12] M.H. Lee, J. H Kim, S.B. Park, Analysis of a scan conversionalgorithm for a real time sector scanner, IEEE Trans. Med. Imag. MI-5 (1986) 96–105.

[13] W.D. Richard, R.M. Arthur, Real-time ultrasonic scan conversionvia linear interpolation of oversampled vectors, Ultrason. Imag. 16(1994) 109–123.

[14] C. Fritsch, M. Parrilla, O. Martınez, D. Jimenez, A multirate scanconversion method, Ultrasonics 38 (2000) 179–182.

[15] J.S. Hwang, T.K. Song, A study of the display pixel-based focusingmethod in ultrasound imaging, Ultrason. Imag. 22 (2001) 1–18.

[16] J.A. Jensen, Field: a program for simulating ultrasound system, in:10th Nordic–Baltic Conference on Biomedical Imaging, vol. 4, 1996,pp. 351–353.

[17] T.I. Laasko, V. Valimaki, M. Karjalainen, U.K. Laine, Splitting theunit delay, IEEE Signal Process. Mag. 13 (1996) 30–60.

[18] J.H. Chang, J.T. Yen, K.K. Shung, A novel envelope detector forhigh-frame rate, high-frequency ultrasound imaging, IEEE Trans.Ultrason. Ferroelect. Freq. Contr. 54 (2007) 1792–1801.

[19] J.M. Cannata, T.A. Ritter, W.-H. Chen, R.H. Silverman, K.K.Shung, Design of efficient, broadband single-element (20–80 MHz)ultrasonic transducers for medical imaging applications, IEEE Trans.Ultrason. Ferroelect. Freq. Contr. 50 (2003) 1548–1557.

high-speed digital scan converter for high-frequency ultrasound sector scanners

Documents