Method to resolve ambiguities in a phase measurement

• US 5,774,089 A
• Filed: 03/13/1997
• Issued: 06/30/1998
• Est. Priority Date: 03/15/1996
• Status: Expired due to Fees

• Current Assignee: Deutsche Telekom AG
• Original Assignee: Deutsche Telekom AG
• Inventors: Davidson, Gordon, Bamler, Richard
• Primary Examiner(s): Sotomayor, John B.
• Application Number:
  US08/816,639
• Time in Patent Office: 474 Days
• Field of Search: 342/25, 342/21, 342/89, 342/156, 342/162, 342/191, 342/192, 342/193, 342/194, 342/195, 342/196, 342/203
• US Class Current: 342/25.00C
• CPC Class Codes: G01J 9/02 by interferometric methods using interferometers for measuring optically the linear dimensions of objects G01B9/02
• CPC Class Codes: G01S 13/89 for mapping or imaging
• CPC Class Codes: G01S 3/48 the waves arriving at the antennas being continuous or intermittent and the phase difference of signals derived therefrom being measured
• CPC Class Codes: G01S 7/295 Means for transforming co-ordinates or for evaluating data, e.g. using computers
• CPC Class Codes: H03H 21/0012 Digital adaptive filters

Abstract

In a method to resolve ambiguities in a phase measurement for application in radar interferometry, a frequency estimation method is used, starting from conjugate complex products of pairs of adjacent pixels in an interferogram. The resolution of these products is subsequently reduced through successive addition or averaging, after which the differential phase of adjacent resolution levels is determined in each resolution level. The sum of the phase differences yields the estimated value for the phase gradient which is then used in a known method, such as the least-squares method, to reconstruct the absolute phase, thus resolving the phase ambiguities. The method according to the invention serves to resolve phase ambiguities in radar interferograms without producing the known distortions produced by the existing methods. The method is also robust at low coherence values as they occur in repeat-pass interferometry where the existing methods fail. The method allows for a simple adaptation to the common local variations in interferogram quality.

Claims

1. A method for resolving ambiguities in a phase measurement in radar interferometry, comprising the steps of:

(a) providing radar data of a two-dimensional image matrix including pixels indexed by i and k;

(b) forming an interferogram z(i,k) from the radar data;

(c) providing a shifter and an adder;

(d) forming from the interferogram in the shifter and the adder a first product

space="preserve" listing-type="equation">C.sub.0.sup.i (i,k)=z(i+1,k)·

z*(i,k)

and a second product

space="preserve" listing-type="equation">C.sub.0.sup.k (i,k)=z(i,k+1)·

z*(i,k),

wherein z* denotes a complex conjugate of z;

(e) providing a multi-resolution unit (3);

(f) subsequently reducing resolution of the first product and the second product by N increments in the multi-resolution unit, the step of reducing resolution including at least one of

a step of averaging adjacent pixels and

a step of adding adjacent pixels;

(g) providing a phase determination unit (4);

(h) forming differential phases, between pairs of adjacent resolution levels in the phase determination unit, sequentially according to

space="preserve" listing-type="equation">δ

.sub.N.sup.i,k (i,k)=arg {C.sub.N.sup.i,k (i,k)},

space="preserve" listing-type="equation">δ

.sub.N-1.sup.i,k (i,k)=arg {C.sub.N-1.sup.i,k (i,k)·

C.sub.N.sup.i,k* (i,k)},

and in general

space="preserve" listing-type="equation">δ

.sub.n.sup.i,k (i,k)=arg {C.sub.n.sup.i,k (i,k)·

C.sub.n+1.sup.i,k* (i,k)},

wherein superscript letters i, k indicate that an equation applies to both indices i, k,

C_n is a function produced by an nth step of the resolution reduction, and

δ

_nⁱ,k is a differential phase of the function C_n to C_n+1, where

n=1, 2, 3 . . . N;

(i) providing a summation unit (5);

(j) determining estimated gradient values

∇

ψ

(i,k)

of a phase gradient field by adding the differential phases in the summation unit from a lowest resolution level N to a predetermined resolution level n_min ;

(k) providing a reconstruction unit (6); and

finally

(l) reconstructing, in the reconstruction unit, an absolute phase φ

from the estimated gradient values of the phase gradient field, whereby the ambiguities are resolved.

2. The method according to claim 1, including a step of reducing a density of the image matrix by factors M_i and M_k in respective coordinates i and k, wherein the number of added adjacent pixels is M_i and M_k.

3. The method according to claim 1, including a step of adding an odd number of pixel values from a next-higher resolution level, wherein the density and dimension fo the image matrix are maintained.

4. The method according to claim 1, wherein the step of determining estimated gradient values includes a step of including phases of high resolution level in a determination of the phase gradient in the summation unit (5) and the phases of high resolution level functionally depend on a locally varying quality measure in the interferogram.

7. The method according to claim 1, wherein the step of forming from the interferogram in the shifter and the adder includes forming a first product

5. The method according to claim 5, wherein the locally varying quality measure in the interferogram is coherence.

6. The method according to claim 5, wherein the step of determining estimated gradient values includes a step of determining whether a solenoidal component of the estimated gradient value is below a predetermined threshold.

8. A method for resolving ambiguities in a phase measurement in radar interferometry, comprising the steps of:

(a) providing radar data of a two-dimensional image matrix including pixels indexed by i and k;

(b) forming an interferogram z(i,k) from the radar data;

(c) forming from the interferogram a first product

space="preserve" listing-type="equation">C.sub.0.sup.i (i,k)=z(i+1,k)·

z*(i,k)

and a second product

space="preserve" listing-type="equation">C.sub.0.sup.k (i,k)=z(i,k+1)·

z*(i,k),

wherein z* denotes a complex conjugate of z;

(d) subsequently reducing resolution of the first product and the second product by N increments, the step of reducing resolution including at least one of

a step of averaging adjacent pixels and

a step of adding adjacent pixels;

(e) forming differential phases, between pairs of adjacent resolution levels, sequentially according to

space="preserve" listing-type="equation">δ

.sub.N.sup.i,k (i,k)=arg {C.sub.N.sup.i,k (i,k)},

space="preserve" listing-type="equation">δ

.sub.N-1.sup.i,k (i,k)=arg {C.sub.N-1.sup.i,k (i,k)·

C.sub.N.sup.i,k* (i,k)},

and in general

space="preserve" listing-type="equation">δ

.sub.n.sup.i,k (i,k)=arg {C.sub.n.sup.i,k (i,k)·

C.sub.n+1.sup.i,k* (i,k)},

wherein superscript letters i, k indicate that an equation applies to both indices i, k,

C_n is a function produced by an nth step of the resolution reduction, and

δ

_nⁱ,k is a differential phase of the function C_n to C_n+1, where

n=1, 2, 3 . . . N;

(f) determining estimated gradient values

∇

ψ

(i,k)

of a phase gradient field by adding the differential phases from a lowest resolution level N to a predetermined resolution level n_min ; and

finally

(g) reconstructing an absolute phase φ

from the estimated gradient values of the phase gradient field, whereby the ambiguities are resolved.