Method for measuring spectral noise densities beyond instrument capability with deterministic confidence levels

1. A method for measuring spectral noise densities below a noise floor of a measuring instrument, the method comprising:

constructing a reference spectral noise density distribution;

constructing a sum spectral noise density distribution;

extracting a spectral noise density distribution from the reference spectral noise density distribution and the sum spectral noise density distribution;

determining a confidence interval associated with the extracted spectral noise density distribution based on a desired confidence level; and

storing the extracted spectral noise density distribution and the confidence interval.

2. The method of claim 1 , wherein said constructing a reference spectral noise density distribution includes acquiring a fully-averaged reference spectral noise density trace.

3. The method of claim 2 , wherein said constructing a reference spectral noise density distribution further includes estimating a plurality of reference statistical parameters from the fully-averaged reference spectral noise density trace.

4. The method of claim 3 , wherein said constructing a reference spectral noise density distribution includes constructing a reference spectral noise density distribution based on the plurality of reference statistical parameters associated with the fully-averaged reference spectral noise density trace.

5. The method of claim 1 , wherein said constructing a sum spectral noise density distribution includes acquiring a fully-averaged sum spectral noise density trace.

6. The method of claim 5 , wherein said constructing a sum spectral noise density distribution further includes estimating a plurality of sum statistical parameters from the fully-averaged sum spectral noise density trace.

7. The method of claim 6 , wherein said constructing a sum spectral noise density distribution includes constructing a sum spectral noise density distribution based on the plurality of sum statistical parameters associated with the fully-averaged sum spectral noise density trace.

8. The method of claim 1 , wherein said determining a confidence interval based on a desired confidence level includes integrating both tails of the extracted spectral noise density distribution based on the desired confidence level to determine an upper bound and a lower bound corresponding to a two-sided confidence interval.

9. The method of claim 1 , wherein said determining a confidence interval based on a desired confidence level includes integrating a tail of the extracted spectral noise density distribution based on the desired confidence level to determine an upper bound corresponding to a one-sided confidence interval.

10. The method of claim 1 , further comprising:

computing an extracted mean of a spectral noise density; and

determining a desired spectral noise density measurement based on the extracted mean of the spectral noise density and the confidence interval.

11. The method of claim 1 , further comprising measuring spectral noise densities at or above the noise floor of the measuring instrument.

12. A measurement instrument comprising:

means for constructing a reference spectral noise density distribution;

means for constructing a sum spectral noise density distribution;

means for extracting a spectral noise density distribution from the reference spectral noise density distribution and the sum spectral noise density distribution;

means for determining a confidence interval associated with the extracted spectral

noise density distribution based on a desired confidence level; and

means for storing the extracted spectral noise density distribution and the confidence interval.

13. The measurement instrument of claim 12 , further comprising means for acquiring a fully-averaged reference spectral noise density trace.

14. The measurement instrument of claim 13 , wherein the means for constructing a reference spectral noise density distribution further comprises estimating a plurality of reference statistical parameters from the fully-averaged reference spectral noise density trace.

15. The measurement instrument of claim 14 , wherein the means for constructing a reference spectral noise density distribution further comprises constructing a reference spectral noise density distribution based on the plurality of reference statistical parameters associated with the fully-averaged reference spectral noise density trace.

16. The measurement instrument of claim 12 , further comprising means for acquiring a fully-averaged sum spectral noise density trace.

17. The measurement instrument of claim 16 , wherein the means for constructing a sum spectral noise density distribution further comprises estimating a plurality of sum statistical parameters from the fully-averaged sum spectral noise density trace.

18. The measurement instrument of claim 17 , wherein the means for constructing a sum spectral noise density distribution further comprises constructing a sum spectral noise density distribution based on the plurality of sum statistical parameters associated with the fully-averaged sum spectral noise density trace.

19. The measurement instrument of claim 12 , wherein the means for determining a confidence interval based on a desired confidence level further comprises integrating both tails of the extracted spectral noise density distribution based on the desired confidence level to determine an upper bound and a lower bound corresponding to a two-sided confidence interval.

20. The measurement instrument of claim 12 , wherein the means for determining a confidence interval based on a desired confidence level further comprises integrating a tail of the extracted spectral noise density distribution based on the desired confidence level to determine an upper bound corresponding to a one-sided confidence interval.

21. The measurement instrument of claim 12 , further comprising:

means for computing an extracted mean of a spectral noise density; and

means for determining a desired spectral noise density measurement based on the extracted mean of the spectral noise density and the confidence interval.

22. A method for measuring spectral noise densities below a noise floor of a measuring instrument, the method comprising:

acquiring a fully-averaged reference spectral noise density trace;

estimating a plurality of reference statistical parameters from the fully-averaged reference spectral noise density trace;

constructing a reference spectral noise density distribution based on the plurality of reference statistical parameters associated with the fully-averaged reference spectral noise density trace;

acquiring a fully-averaged sum spectral noise density trace;

estimating a plurality of sum statistical parameters from the fully-averaged sum spectral noise density trace;

constructing a sum spectral noise density distribution based on the plurality of sum statistical parameters associated with the fully-averaged sum spectral noise density trace;

extracting a spectral noise density distribution from the reference spectral noise density distribution and the sum spectral noise density distribution;

determining a confidence interval associated with the extracted spectral noise density distribution based on a desired confidence level; and

storing the extracted spectral noise density distribution and the confidence interval.

23. A computer readable medium comprising program instructions for measuring spectral noise densities below a noise floor of a measuring instrument, wherein the program instructions are computer executable to:

construct a reference spectral noise density distribution;

construct a sum spectral noise density distribution;

extract a spectral noise density distribution from the reference spectral noise density distribution and the sum spectral noise density distribution;

determine a confidence interval associated with the extracted spectral noise density distribution based on a desired confidence level; and

store the extracted spectral noise density distribution and the confidence interval.