## Abstract

We investigate the accuracy of the femtosecond pulse-retrieval technique called phase and intensity from correlation and spectrum only (PICASO). Different versions of this technique that make use of balanced and unbalanced intensity and interferometric correlations are compared with respect to the rms phase and the intensity error. The effect of measurement noise on the phase and amplitude retrieval is studied, and the results are compared with other retrieval methods.

© 2002 Optical Society of America

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### Equations (17)

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(1)
$$\mathrm{\Delta}={\left\{\frac{1}{N}\sum _{i=1}^{N}[{A}_{m}({\tau}_{i})-{A}_{r}({\tau}_{i}){]}^{2}\right\}}^{1/2}.$$
(2)
$$A(\tau )=1+2{A}_{0}(\tau )+2\mathrm{Re}[{A}_{1}(\tau )exp(-i{\omega}_{0}\tau )]+\mathrm{Re}[{A}_{2}(\tau )exp(-2i{\omega}_{0}\tau )],$$
(3)
$${A}_{0}(\tau )={\int}_{-\infty}^{\infty}{I}_{1}(t){I}_{2}(t-\tau )\mathrm{d}t,$$
(4)
$${A}_{1}(\tau )={\int}_{-\infty}^{\infty}[{I}_{1}(t)+{I}_{2}(t-\tau )]{E}_{1}(t){E}_{2}^{*}(t-\tau )\mathrm{d}t,$$
(5)
$${A}_{2}(\tau )={\int}_{-\infty}^{\infty}{E}_{1}^{2}(t){E}_{2}^{*2}(t-\tau )\mathrm{d}t,$$
(6)
$$B(\tau )=1+9{B}_{0}(\tau )+3\mathrm{Re}[{B}_{1}(\tau )exp(-i{\omega}_{0}\tau )]+3\mathrm{Re}[{B}_{2}(\tau )exp(-2i{\omega}_{0}\tau )]+\mathrm{Re}[{B}_{3}(\tau )exp(-3i{\omega}_{0}\tau )],$$
(7)
$${B}_{0}(\tau )={\int}_{-\infty}^{\infty}[{I}_{1}^{2}(t){I}_{2}(t-\tau )+{I}_{1}(t){I}_{2}^{2}(t-\tau )]\mathrm{d}t,$$
(8)
$${B}_{1}(\tau )={\int}_{-\infty}^{\infty}\{[{I}_{1}^{2}(t)+{I}_{2}^{2}(t-\tau )]{E}_{1}(t){E}_{2}^{*}(t-\tau )+3{I}_{1}(t){I}_{2}(t-\tau ){E}_{1}(t){E}_{2}^{*}(t-\tau )\}\mathrm{d}t,$$
(9)
$${B}_{2}(\tau )={\int}_{-\infty}^{\infty}[{I}_{1}(t)+{I}_{2}(t-\tau )]{E}_{1}^{2}(t){E}_{2}^{*2}(t-\tau )\mathrm{d}t,$$
(10)
$${B}_{3}(\tau )={\int}_{-\infty}^{\infty}{E}_{1}^{3}(t){E}_{2}^{*3}(t-\tau )\mathrm{d}t.$$
(11)
$${B}_{0}(\tau )={\int}_{-\infty}^{\infty}[{\alpha}^{2}{I}^{2}(t)I(t-\tau )+{\alpha}^{4}{I}^{2}(t-\tau )I(t)]\mathrm{d}t.$$
(12)
$$\mathrm{\Phi}(\omega )=\sum _{i=2}^{n}{\varphi}_{i}(\omega -{\omega}_{0}{)}^{i}.$$
(13)
$$\mathrm{\Phi}(\omega )={\varphi}_{e}(\omega )+{\varphi}_{o}(\omega ).$$
(14)
$${\epsilon}_{I}={\left\{\frac{1}{N}\sum _{i=1}^{N}[{I}_{t}({\tau}_{i})-{I}_{r}({\tau}_{i}){]}^{2}\right\}}^{1/2},$$
(15)
$${\epsilon}_{\varphi}=\frac{{\left\{\frac{1}{N}\sum _{i=1}^{N}{I}_{t}^{2}({\tau}_{i})[{\varphi}_{t}({\tau}_{i})-{\varphi}_{r}({\tau}_{i}){]}^{2}\right\}}^{1/2}}{{\left\{\frac{1}{N}\sum _{i=1}^{N}{I}_{t}^{2}({\tau}_{i})\right\}}^{1/2}}.$$
(16)
$${A}_{m}^{\prime}({\tau}_{i})=[1+{\xi}_{m}(f)]{A}_{m}({\tau}_{i})+f\frac{{\xi}_{a}(n)}{n},$$
(17)
$${S}^{\prime}({\omega}_{i})=[1+{\xi}_{m}(f)]S({\omega}_{i})+f\frac{{\xi}_{a}(n)}{n},$$