Method of measuring a physical function using a composite function which includes the physical function and an arbitrary reference function

A method of measuring a nonlinearity profile of a sample, the method comprising:

• providing a sample having at least one sample surface and having a sample nonlinearity profile along a sample line through a predetermined point on the sample surface, the sample line oriented perpendicularly to the sample surface;
• measuring a Fourier transform of the sample nonlinearity profile;
• providing a reference material having at least one reference surface and having a reference nonlinearity profile along a reference line through a predetermined point on the reference surface, the reference line oriented perpendicularly to the reference surface;
• obtaining a Fourier transform of the reference nonlinearity profile;
• forming a first composite sample having a first composite nonlinearity profile by placing the sample and the reference material proximate to one another in a first configuration with the sample line substantially collinear with the reference line;
• measuring a Fourier transform of the first composite nonlinearity profile;
• forming a second composite sample having a second composite nonlinearity profile which is inequivalent to the first composite nonlinearity profile by placing the sample and the reference material proximate to one another in a second configuration with the sample line substantially collinear with the reference line;
• measuring a Fourier transform of the second composite nonlinearity profile;
• and
• using the Fourier transforms of the sample nonlinearity profile, the reference nonlinearity profile, the first composite nonlinearity profile, and the second composite nonlinearity profile to calculate the sample nonlinearity profile.

A method of measuring a sample temporal waveform of a sample optical pulse, the method comprising:

• providing a sample optical pulse having a sample temporal waveform;
• measuring a Fourier transform of the sample temporal waveform;
• providing a reference optical pulse having a reference temporal waveform;
• obtaining a Fourier transform of the reference temporal waveform;
• forming a first composite optical pulse comprising the sample optical pulse followed by the reference optical pulse, the first composite optical pulse having a first composite temporal waveform;
• measuring the Fourier transform of the first composite temporal waveform;
• providing a time-reversed pulse having a time-reversed temporal waveform corresponding to the reference temporal waveform after being time-reversed;
• forming a second composite optical pulse comprising the sample optical pulse followed by the time-reversed optical pulse;
• measuring the Fourier transform of the second composite temporal waveform;
• and
• calculating the sample temporal waveform using the Fourier transform of the sample temporal waveform, the Fourier transform of the reference temporal waveform, the Fourier transform of the first composite temporal waveform, and the Fourier transform of the second composite temporal waveform.