Calculation of point spread functions

The calculation of point spread functions is done by placing a point in front of the transducer and then sweeping the beam over the point. This gives the point spread function of the imaging system. Field II can make this calculation for a number of points simultaneously and thereby reveal the dynamic focusing properties of the imaging system. A point phantom has been made for this purpose. It consists of a number of point targets placed with a distance of 5 mm starting at 15 mm from the transducer surface.

A linear sweep image is then made of the points and the resulting image is compressed to show a 60 dB dynamic range. This phantom is suited for showing the spatial variation of the point spread function for a particular transducer, focusing, and apodization scheme.

Twelve examples of using this phantom is shown in the figures below. The top graphs show imaging without apodization and the bottom graphs show when a Hanning window is used for apodization in both transmit and receive. A 128 elements transducer with a nominal frequency of 3 MHz was used. The element height was 5 mm, the width was a wavelength and the kerf 0.1 mm. The excitation of the transducer consisted of 2 periods of a 3 MHz sinusoid with a Hanning weighting, and the impulse response of both the emit and receive aperture also was a two cycle, Hanning weighted pulse. In the graphs A - C, 64 of the transducer elements was used for imaging, and the scanning was done by translating the 64 active elements over the aperture and focusing in the proper points. In graph D and E 128 elements were used and the imaging was done solely by moving the focal points.

Graph A uses only a single focal point at 60 mm for both emission and reception. B also uses reception focusing at every 20 mm starting from 30 mm. Graph C further adds emission focusing at 10, 20, 40, and 80 mm. D applies the same focal zones as C, but uses 128 elements in the active aperture.

The focusing scheme used for E and F applies a new receive profile for each 2 mm. For analog beamformers this is a small zone size. For digital beamformers it is a large zone size. Digital beamformer can be programmed for each sample and thus a "continuous" beam tracking can be obtained. In imaging systems focusing is used to obtain high detail resolution and high contrast resolution preferably constant for all depths. This is not possible, so compromises must be made. As an example figure F shows the result for multiple transmit zones and receive zones, like E, but now a restriction is put on the active aperture. The size of the aperture is controlled to have a constant F-number (depth of focus in tissue divided by width of aperture), 4 for transmit and 2 for receive, by dynamic apodization. This gives a more homogeneous point spread function throughout the full depth. Especially for the apodized version. Still it can be seen that the composite transmit can be improved in order to avoid the increased width of the point spread function at e.g. 40 and 60 mm.

The resulting images are:

Point spread function phantom imaged without apodization.

Point spread function phantom imaged with apodization.

The m-files for calculating the images can be found at:

The routine field.m initializes the field system, and should be modified to point to the directory holding the Field II code and m-files. The routine pnt_img.m is then called to calculate the different point spread function. The phantom data is contained in pts_pha.m and the routine mk_img.m makes the individual gray scale displays. The other routines are used for setting the parameters for the different focusing and apodization schemes.

The example can easily be modified to scan any phantom defined as a collection of point targets. This can be done by modifying the file pts_pha.m.