Calibration of frequency monitors having dual etalon signals in quadrature

• US 7,813,886 B2
• Filed: 12/04/2007
• Issued: 10/12/2010
• Est. Priority Date: 12/07/2006
• Status: Active Grant

• Current Assignee: Picarro, Inc.
• Original Assignee: Picarro, Inc.
• Inventors: Tan, Sze Meng
• Primary Examiner(s): Bui; Bryan
• Application Number:
  US11/999,375
• Publication Number:
  US 20080137089A1
• Time in Patent Office: 1,043 Days
• Field of Search: 702/85, 702/95, 702/106, 356/352, 356/454
• US Class Current: 702/85
• CPC Class Codes: G01J 9/02 by interferometric methods using interferometers for measuring optically the linear dimensions of objects G01B9/02
• CPC Class Codes: H01S 5/0687 Stabilising the frequency of the laser

Abstract

Improved calibration of a dual-etalon frequency monitor having x-y outputs is provided. An ellipse is fit to the (x,y) points from a set of calibration data. For each (x,y) point, an angle θ is determined. A linear fit of frequency to θ is provided. Differences between this linear fit and the determined values of θ are accounted for by including a spline fit to this difference in the calibration.

Claims

1. A method of calibrating a frequency monitor having dual etalon signals in quadrature, the method comprising:

a) providing calibration data in the form of triples (x_i, y_i, ν

_i) indexed by i, wherein for each triple, x_i is a first etalon signal at a known frequency ν

_i and y_i is a second etalon signal at said known frequency ν

_i, and wherein said first and second etalon signals are substantially in quadrature;

b) fitting an ellipse to the set of points (x_i, y_i), wherein said ellipse is parametrically defined according to

x=x₀+A cos θ

y=y₀+B sin(θ

+ε

);

c) calculating an angle parameter θ

_i of said ellipse for each of said points (x_i, y_i);

d) fitting a line to the set of points (θ

_i, ν

_i) to provide a linear angle-frequency fit, wherein said line is parametrically defined according to ν

=sθ

+ν

₀;

e) providing said parameters s and ν

₀ and said parameters A, B, x₀, y₀, and ε

as ν

(θ

) calibration outputs;

f) calibrating said frequency monitor having dual etalon signals in quadrature using said ν

(θ

) calibration outputs.

2. The method of claim 1, further comprising:

g) determining a difference e_i of said linear angle-frequency fit at each of said triples according to ε

=ν

_i−

(sθ

_i+ν

₀);

h) fitting a spline to the set of points (θ

_i, e_i) to provide a spline difference fit e(θ

);

i) providing said spline difference fit e(θ

) as part of said ν

(θ

) calibration outputs.

3. The method of claim 1, wherein said calculating an angle parameter θ

_i of said ellipse for each of said points (x_i, y_i) comprises setting θ

_i=a tan 2(A(y_i−

y₀)−

B(x_i−

x₀)sin ε

, B(x_i−

x₀)cos ε

).

4. The method of claim 1, wherein said frequencies ν

_i of said calibration data are equally spaced.

5. The method of claim 4, wherein said frequencies ν

_i of said calibration data are determined by a reference optical cavity.

6. The method of claim 1, wherein said fitting an ellipse comprises:

fitting a quadratic form a₀x²+a₁xy+a₂y²+a₃x+a₄y+a₅=0 to said set of points (x_i, y_i) to provide values for fitting parameters a₀, a₁, a₂, a₃, a₄, and a₅;

calculating values for x₀, y₀, A, B, and ε

, from said fitting parameters a₀, a₁, a₂, a₃, a₄, and a₅.

7. The method of claim 2, wherein said fitting a spline comprises fitting cubic B-splines defined on a uniformly spaced set of knots.

8. A method of measuring an operating frequency of an optical source in a system including a frequency monitor having dual etalon signals in quadrature, the method comprising:

calibrating said frequency monitor according to the method of claim 1;

measuring source operating data (x_op, y_op), wherein x_op and y_op are respectively said first and second etalon signals provided by said frequency monitor responsive to radiation from said optical source having said operating frequency;

calculating an angle parameter θ

_op of said optical source according to a θ

_op=a tan 2(A(y_op−

y₀)−

B(x_op−

x₀)sin ε

, B(x_op−

x₀)cos ε

);

determining said operating frequency from said ν

(θ

) calibration outputs and from said angle parameter θ

_op;

providing said determined operating frequency as an output.

9. The method of claim 8, wherein said determining said operating frequency from said ν

(θ

) calibration outputs and from said angle parameter θ

_op comprises;

providing a secondary measurement of said operating frequency;

defining a set of angles θ

_n=θ

_op+2π

n, where n is any integer that results in θ

_n being within a predetermined calibration range;

calculating a set of frequencies ν

_n=θ

(θ

_n) from said ν

(θ

) calibration outputs and from said set of angles θ

_n;

selecting one of said set of frequencies ν

_n as said determined operating frequency according to said secondary measurement.

10. A method of setting an optical source to operate at or near a predetermined frequency in a system including a frequency monitor having dual etalon signals in quadrature, the method comprising:

calibrating said frequency monitor according to the method of claim 2;

determining an angle θ

_in corresponding to said predetermined frequency ν

_in from said ν

(θ

) calibration outputs;

controlling the output frequency of said optical source such that w₁(x−

x₀)+w₂(y−

y₀)=0, wherein x and y are said first and second etalon signals respectively, and wherein

11. The method of claim 10, further comprising:

providing coarse frequency control of said optical source sufficient to distinguish said predetermined frequency ν

_in from any frequency ν

_n=ν

(θ

_in+2π

n), where n can be any non-zero integer;

wherein said frequencies ν

_n are determined from said corresponding angles θ

_in+2π

n according to said ν

(θ

) calibration outputs.

12. A method of calibration update in a system having a frequency monitor having dual etalon signals in quadrature, the method comprising:

setting an optical source to operate at or near each of a set of predetermined frequencies ν

_j according to the method of claim 10;

measuring an output frequency error Δ

ν

_j=ν

_j,out−

ν

_j at each of said set of predetermined frequencies, where ν

_j,out is optical source frequency when said source is set to operate at ν

_j, wherein ν

_j,out is measured independently of said ν

(θ

) calibration outputs;

revising said spline difference fit e(θ

) to decrease said output frequency error, by making incremental changes to spline fit coefficients.

13. The method of claim 12, wherein said revising said spline difference fit is repeated one or more times.

14. A method of calibrating a wavelength monitor having dual etalon signals in quadrature, the method comprising:

a) providing calibration data in the form of triples (x_i, y_i, λ

_i) indexed by i, wherein for each triple, x_i is a first etalon signal at a known wavelength λ

_i and y_i is a second etalon signal at said known wavelength λ

_i, and wherein said first and second etalon signals are substantially in quadrature;

b) fitting an ellipse to the set of points (x_i, y_i), wherein said ellipse is parametrically defined according to

x=x₀+A cos θ

y=y₀+B sin(θ

+ε

);

c) calculating an angle parameter θ

_i of said ellipse for each of said points (x_i, y_i);

d) fitting a line to the set of points (θ

_i, λ

_i) to provide a linear angle-wavelength fit, wherein said line is parametrically defined according to λ

=sθ

+λ

₀;

e) providing said parameters s and λ

₀ and said parameters A, B, x₀, y₀, and ε

as λ

(θ

) calibration outputs;

f) calibrating said wavelength monitor having dual etalon signals in quadrature using said λ

(θ

) calibration outputs.

15. The method of claim 14, further comprising:

g) determining a difference e_i of said linear angle-wavelength fit at each of said triples according to e_i=λ

_i−

(sθ

_i+λ

₀);

h) fitting a spline to the set of points (θ

_i, e_i) to provide a spline difference fit e(θ

);

i) providing said spline difference fit e(θ

) as part of said λ

(θ

) calibration outputs.