Acoustic Lens System

Abstract

An acoustic lens system having a plurality of acoustic lens elements with the lens elements having respective thermal dispersion factors. The acoustic lens elements are fabricated in accordance with a predetermined relationship of the respective thermal dispersion factors such that the focal length of the acoustic lens system is maintained at a substantially constant value throughout a wise temperature variation. This temperature insensitive result is additionally achieved by a lens system wherein the lens elements are spaced at a precalculated distance from one another.

Description

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention in general relates to acoustic systems, and more particularly to a system which focuses acoustic energy by means of acoustic lens elements.

2. Description of the Prior Art

Acoustic lens systems are utilized in various fields such as sonar, ultrasonic inspection systems, and medical diagnosis and treatment, to name a few. The lens system is generally utilized to obtain directivity or resolution and includes one or more acoustic lens element of a solid or liquid material.

Each acoustic lens element has an associated index of refraction, n, which usually changes radically with temperature variations. This variation of n with respect to temperature, in turn varies the focal length of each particular lens element, and accordingly the focal length of the acoustic lens system. For optimum operation a transducer means is placed at the focal point of the acoustic lens system, and since the focal point is determined by the focal length, the transducer means becomes improperly situated due to the focal point changing with temperature. This particular situation is intolerable for certain applications, such as high resolution sonar systems.

It is therefore a primary object of the present invention to provide an acoustic lens system which is relatively insensitive to temperature variations.

SUMMARY OF THE INVENTION

Basically an acoustic lens system is provided which includes a plurality of acoustic lens elements having different thermal dispersion factors .phi. to compensate for the change of index of refraction, to thereby maintain the focal length of the acoustic lens system at a fairly constant value over a wide temperature range. A system focal length is initially chosen and materials having certain indices of refraction and thermal dispersion factors are then selected for fabricating the acoustic lens elements and with the proper selection, the desired result is achieved. For acoustic lens systems where it is desired or convenient to utilize acoustic lens elements of the same material, the lens elements are spaced by a predetermined distance related to their individual focal lengths, which serves to maintain the focal length of the acoustic lens system relatively constant.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a view of a single-element lens system illustrating a possible change in focal length due to a temperature variation;

FIG. 2 is a view of a double-element lens system illustrating the same phenomenon;

FIG. 3 is a curve illustrating the change in focal length as a function of temperature of a typical acoustic lens system;

FIG. 4 is a curve illustrating the index of refraction of two different materials and how the index changes with temperature;

FIG. 5 is one lens system according to the teachings of the present invention;

FIG. 6 is a curve of focal length as a function of temperature of a typical acoustic lens system according to the teachings of the present invention;

FIGS. 7 and 10 illustrate other two-element lens systems according to the teachings of the present invention;

FIGS. 8, 9, 11 and 12 illustrate other embodiments utilizing three acoustic lens elements; and

FIG. 13 illustrates another embodiment of the invention wherein temperature compensation is achieved by correct spacing of the lens elements.

DESCRIPTION OF THE PREFERRED EMBODIMENT

In FIG. 1 there is illustrated an acoustic lens element 10 bounded by a first curved surface 11 having a radius of curvature r.sub.1 and a second curved surface 12 having a radius of curvature r.sub.2. If a distant sound source produces acoustic energy which impinges upon the lens element 10 in parallel ray paths 14, parallel to the lens axis, then that sound source may be considered to be at infinity and the ray paths after refraction by the lens element 10 converge to a point called the focal point at a distance f from the lens element, f being the focal length.

Determination of the focal length f may be made by the following equation:

A problem arises however in that the index of refraction, n, is not constant but varies with temperature so that the focal length varies with temperature. If the temperature for example is at some value a, then the focal point, as illustrated in FIG. 1 will be at point f.sub.a. If the temperature increases, the value of n increases and the focal point at some higher temperature b will be located at position f.sub.b.

If the source of acoustic energy is at a distance less than an effective infinity, then the ray path will converge to a point called the image or focal point at a distance other than the focal length. If the distance (measured from the center of the lens element) to the source of acoustic energy is s.sub.0 and the distance to the focal point is s.sub.i then the relation between the focal length source distance and focal point is as follows:

1/f=1/s.sub.0 +1/s.sub.i Equation (2)

With relatively small radii of curvature of the lens surfaces a situation develops wherein the ray paths do not all intersect at a common focal point. This undesirable situation is known as spherical aberration. To reduce spherical aberration acoustic lens systems have been built which utilize two or more lens elements and to provide for certain focus characteristics, the lens elements have had different indices of refraction n. A two element system is illustrated in FIG. 2. A first lens element 17 is of the convex variety having a second surface which matches the curvature of the first surface of a second lens element 20 of the concave variety. Acoustic energy represented by the ray paths 22 is focused, at a temperature a, to a focal point f.sub.a. In ultrasonic testing or in the medical field, the apparatus is generally utilized in an environment which maintains a relatively constant temperature and the focal point substantially remains at f.sub.a. Transducer means therefore at f.sub.a will be at the convergence of ray paths 22 and will properly detect such energy, or conversely if utilized as a transmitter, transducer means at f.sub.a will provide acoustic energy represented by ray paths 22.

If the apparatus of FIG. 2 is utilized in an environment where the temperature may change radically, such as in oceanographic uses, then the focal point will change such as to position f.sub.b with an increase to a temperature b such that the transducer means is no longer located at a position for proper transmission or reception of acoustic energy.

The focal length of the dual element system of the FIG. 2 may be determined knowing the focal length of each individual lens element 17 and 20 and the distance between them. The relationship is given by the following formula:

1/f=1/f'+1/f"-L/f'f" Equation (3)

In equation (3), f is the focal length of the lens system at a particular temperature; f' is the focal length of lens element 17 at that same temperature; f" is the focal length of lens element 20 at that temperature; and L is the distance between the centers of the lens elements. When the lens elements are very close or are touching as in FIG. 2 and L is less than 2 percent of f"+f' then the last term of equation 3 is negligible and may, to a good approximation, be neglected in figuring out the system focal length or may be used to apply a correction factor.

FIG. 3 illustrates a curve of focal length versus temperature for a typical system such as illustrated in FIG. 2. At a temperature of a the system has a focal length of value f.sub.a which drops off sharply to a value f.sub.b at temperature b. For oceanographic work the temperature range from a to b may represent 20.degree. measured on the Centigrade (C) scale. At an intermediate temperature c the system has a focal length f.sub.c. For industrial or medical usage the environmental temperature, and the temperature of the lens elements may vary only by a small amount .DELTA.T' for which change the system focal length will correspondingly vary by a small amount .DELTA.f'. .DELTA.f' may be within tolerable limits whereas a variation from f.sub.a to f.sub.b would result in an inoperative system.

The change in focal length is due to the individual changes in focal length of the lens elements brought about by a changing index of refraction. In FIG. 4 there is illustrated a curve of index of refraction n versus temperature for the two elements of FIG. 2. Curve 17n represents the index of refraction of element 17 and curve 20n represents the index of refraction of element 20. As the temperature increases the indices of refraction increase, however since the elements are of different materials the indices of refraction increase at different rates.

FIG. 5 is illustrative of one embodiment of the present invention wherein two acoustic lens elements 25 and 26 are utilized and are serially disposed in the path of acoustic energy emanating from source 28. Characteristics associated with the first lens element 25 will have primed designations and characteristics associated with the second lens element 26 will have double primed designations. Accordingly, lens element 25 has a first surface 31 with a radius of curvature r'.sub.1, and a second surface 32 with a radius of curvature r'.sub.2. Similarly, lens element 26 has first and second surfaces 34 and 35 with respective radii of curvatures r".sub.1 and r".sub.2. Lens elements 25 and 26 are considered to be thin lenses with the separation between them, L, being negligible.

At a particular temperature, lens element 25 has an acoustic index of refraction n' and lens element 26 has an acoustic index of refraction n". The focal length for the system of FIG. 5 is given by equation (3) and the image or focal point 39, at which is located transducer means, may be determined from equation (2).

In actual construction, each lens element may be of a particular solid, or of a particular liquid contained within a thin shell of material, such as aluminum, forming the surfaces 31, 32, 34, 35. The shells are so thin as to have negligible effect on the passage of acoustic energy.

In order to ensure that the focal point remains substantially at point 39 within a wide variation of temperature the lens elements are designed having certain acoustic indices of refraction in addition to certain thermal dispersion factors. The thermal dispersion factor .phi. for a lens element is a measure of the rate of change of its index of refraction with respect to temperature. An indication of the thermal dispersion factor for a particular lens element is set forth in equation (4) wherein n.sub.a is the value of the index refraction at temperature a; n.sub.b the index of refraction at temperature b; and n.sub.c the index of refraction at some temperature c having a value between a and b.

Each of the terms of the right-hand side of equation (4) may be determined by comparing, at temperatures a, b and c, the velocity of sound through the material with respect to the velocity of sound through a reference, such as water, at those respective temperatures a, b and c. Such determinations are well known to those skilled in the art.

The system is designed such that the focal length does not appreciably vary between two temperatures a and b where b-a may for example be greater than 5.degree. C. This situation is illustrated in FIG. 6 showing a curve of focal length versus temperature wherein the focal length at temperature a is made equal to the focal length at temperature b. Mathematically stated, for the temperature difference, .DELTA.T, between temperatures a and b, .DELTA.f=0. By differentiating equation (3) with respect to temperature and equating it to 0, and with the utilization of equations (1) and (4), it may be mathematically demonstrated that

Where L is the distance between lens elements 25 and 26 (see FIG. 5); .phi.' is the thermal dispersion factor for lens element 25; f" is the focal length for lens element 26 at a temperature such as c intermediate a and b; .phi." is the thermal dispersion for lens element 26; and f' is the focal length at temperature c for the lens element 25. With the lens elements touching one another the L term is negligible and equation 5 reduces to

-.phi.'/.phi."=f'/f" Equation (6)

which states that if the ratio of the focal lengths of the two elements is made equal to the negative of the ratio of the thermal dispersion factors of those two elements, then the focal length of the system is the same at temperatures a and b, representing a temperature difference .DELTA.T. .DELTA.T, by way of example is of a magnitude that would cause a change in the value of n of a lens element, to vary by 1 to 15 percent within that range. At temperature a some typical sound ray paths in FIG. 5 are designated 41 while at temperature b they are designated 41'. Ray paths 41 and 41' converge at the image or focal point 39.

A variation of FIG. 5 is illustrated in FIG. 7 wherein a first lens element 45 and a second lens element 46 have a common surface therebetween. The indices of refraction, and thermal dispersion factors, are such that the designed system focal length will not appreciably vary for changes of temperature between selected temperatures a and b even if such a temperature change would cause any one of the indices of refraction to vary by more than 1 or 2 percent. Within that temperature range acoustic energy emanating from source 48 will image at focal point 50.

As illustrated in FIG. 6 a two-element system makes a maximum excursion of .DELTA.f between temperature limits a and b. In order to reduce the magnitude of .DELTA.f a three-element lens system may be utilized such as illustrated in FIGS. 8 and 9 wherein three lens elements are serially arranged for the passage of acoustic energy with each lens element having a different thermal dispersion factor resulting in a system focal length which does not appreciably vary between a relatively wide temperature variation.

FIG. 10 illustrates an embodiment which includes a first thin lens element 55 in conjunction with a second thick lens element 56. Acoustic energy from a source at point 59 is converged to a focal point 60 located within the second lens element 56. The two lens elements 55 and 56 are of different materials exhibiting different thermal dispersions. Design of such an acoustic lens system in addition to thin lens formulae would include thick lens formulae well known to those skilled in the art.

Extensions of the embodiment of FIG. 10 are illustrated in FIGS. 11 and 12 both of which are three-lens element systems incorporating two thin and one thick lens element.

In situations where an acoustic lens system is to be assembled of lens elements all having the same indices of refraction and thermal dispersion factors, temperature insensitivity may still be achieved by a precise positioning of the lens elements relative to one another. By way of example FIG. 13 illustrates an acoustic lens system having two lens elements 67 and 68 of the same material such that their indices of refraction and thermal dispersion factors are equal. Acoustic energy emanating from a source at an effective infinity converges, as indicated by the ray paths 71, to a focal point 73. The separation between the lens elements is L. In the following derivation characteristics associated with lens element 67 have been given primed designations and characteristic associated with lens element 68 have been given double-primed designations. From equation (1) the focal length for lens element 67 is 1/f'=(n-1) [K.sub.1] where the bracketed term K.sub.1 is equivalent to the bracketed term in equation (1). The focal length of lens element 68 is 1/ f"=(n-1) [K.sub.2 ]. By substituting equations (7) and (8) into equation (3) for determining system focal length f:

1/f=(n-1) (K.sub.1 +K.sub.2)-L (n-1).sup. 2 K.sub.1 K.sub.2 Equation (9)

To make f independent of changes in n, df/dn is set equal to 0. Differentiating equation (9) there is obtained:

-1/ f.sup.2 df/dn=0=K.sub.1 +K.sub.2 -2L(n-1) K.sub.1 K.sub.2 Equation (10)

Multiplying equation (10) by (n-1) results in:

K.sub.1 (n-1) +K.sub.2 (n-1) -2L(n-1) K.sub.1 (n-1) K.sub.2 =0 Equation (11)

From equations (7) and (8), equation (11) is equivalent to:

1/f'+1/ f"-2L/f' f"=0 Equation (12)

And:

L=f'+f"/2 Equation (13)

Thus with two lens elements of the same material separated by a distance L equal to half the sum of the focal length of the individual lens elements, the focal length of the system is independent of the index of refraction and is insensitive to temperature changes. Obviously this technique can be extended to acoustic lens systems having more than two lens elements.

Two techniques have been described for thermal compensation of acoustic lens systems. One technique utilizes acoustic lens elements of different materials having different thermal dispersion factors wherein the system focal length is designed to have a certain value at a first temperature and to have that same value at a second temperature and wherein the thermal dispersion factors bear a predetermined relationship with respect the to the focal length of the individual lens elements. The second technique involves the use of lens elements of the same material with a predetermined separation between lens elements. As would be apparent to those skilled in the art, one may combine the two techniques. In other words, and by way of example, the relationship of equation (6) was derived assuming that L equals 0 and the relationship of equation (13) was derived assuming that the thermal dispersion factors of the lens elements were equal. The two techniques may be combined by utilizing the relationship of equation (5). For example for a two element system and knowing .phi.' and .phi." and with the lens elements design to have individual focal lengths of f' and f",the elements may be separated by a distance L calculatable from equation (5) to minimize changes in system focal length with temperature changes.

Alternatively if the separation between the lens element is fixed at the distance L the thermal dispersion factors and/or the individual focal lengths of the lens elements may be chosen to make the equality of equation (5).

Although the present invention has been described with a certain degree of particularity, it should be understood that the present disclosure has been made by way of example and that modifications and variations of the present invention are made possible in the light of the above teachings.

Claims

I claim:

1. An acoustic lens system having a focal length, comprising:

a. a plurality of acoustic lens elements serially arranged for the passage of acoustic energy;

b. each said lens element having a focal length and an index of refraction;

c. each said lens element having a thermal dispersion factor dependent upon the rate of change of its index of refraction with respect to changes in temperature; and

d. the thermal dispersion factors of, and the distance between, said lens elements being of values to maintain the focal length of said acoustic lens system substantially constant throughout a temperature range wherein said index of refraction would vary by at least 1 percent.

2. A system according to claim 1 which includes

a. a first lens element having a focal length f' and a thermal dispersion factor .phi.';

b. a second lens element having a focal length f" and a thermal dispersion factor .phi.";

c. the separation between said first and second elements being negligible; and

d. said focal lengths and thermal dispersion factors having the relationship

-.phi.'/.phi."=f'/f".

3. A system according to claim 1 wherein

a. each lens element has substantially the same thermal dispersion factor and index of refraction;

b. the separation between at least two lens elements is L; and

c. L=f' +f"/2 where f' and f" are the respective focal lengths of said two lens elements.

4. An acoustic lens system having a focal length, comprising:

a. a plurality of acoustic lens elements serially arranged for the passage of acoustic energy;

b. each said lens element having a focal length and an index of refraction;

c. each said lens element having a thermal dispersion factor dependent upon the rate of change of its index of refraction with respect to changes in temperature; and

d. the thermal dispersion factors of, and the distance between, said lens elements being chosen that the focal length of said acoustic lens system has a value at a first temperature and has substantially that same value at a second temperature more than 5.degree. C. greater than said first temperature.