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An optical biprism combines two shallow prism regions that deflect parts of an incident beam in different directions. In the familiar Fresnel arrangement, associated with Augustin-Jean Fresnel, the regions act like two thin optical prisms placed base to base. Light from one narrow illuminated slit emerges as if from two separated virtual images of that slit. Where the two parts overlap, their optical coherence permits wave interference.^[ref]

This supplies two related optical sources without requiring two independent lamps to maintain a stable phase difference. A bench apparatus uses a narrow slit, the optical biprism, and a movable eyepiece or screen. A micrometer translation measures the spacing of several interference fringes. A convex lens can image the two virtual sources in either of two conjugate positions; if their measured image separations are $d_1,d_2$, their actual full separation is $d=\sqrt{d_1{d}_2}$. The inverse magnifications of the two positions explain the geometric mean.^[ref]

A thin-prism calculation makes the geometry explicit. Let each region have small wedge angle $\alpha$, refractive index $n$ relative to air, and slit-to-prism distance $a$. The paraxial deviation is $\delta \simeq (n-1)\alpha$. Backward extension of the emergent rays locates the virtual sources a distance $a\delta$ above and below the original slit, soAt a screen a further distance $b$ beyond the prism, the source-to-screen distance is $D=a+b$. Near the axis, the optical path difference is $dy/D$, giving interference fringe spacingThe symbols here use $d$ for the full source separation; the apparatus manual uses $2d$ for that same quantity.

For an original chosen model, $n=1.50$, $\alpha =1^{\circ }$, $a=0.10\mathrm{m}$, $b=0.90\mathrm{m}$ and $\lambda =600\mathrm{nm}$ give $d\simeq 1.745\mathrm{mm}$ and $\beta \simeq 0.344\mathrm{mm}$. The wedge angle must be converted to radians in the small-angle formula.

A finite slit width, limited optical coherence, unequal beam intensities and misalignment can reduce fringe visibility. The Wollaston prism instead separates linear polarization components using birefringence; its two beams do not automatically interfere on an ordinary intensity screen because their polarizations are orthogonal.

Optical pulse temporal contrast compares a pulse's peak with weaker light at another time. For a radiant power trace with peak $P_{\max }>0$, explicitly choose either the peak-to-local ratio $C(t)=P_{\max }/P(t)$ or its inverse $r(t)=P(t)/P_{\max }$. The first is at least one where the local power is positive; the second lies between zero and one. With a fixed transverse beam shape, the same ratio can be formed from light intensity. If the beam shape changes with time, specify the spatial sampling instead of identifying local intensity and total power.

A plateau at $10^{-3}$ of the peak has $r=10^{-3}$ and $C=1000$. Expressing this power ratio as optical contrast in decibels givesFor an amplitude ratio $A$ whose power ratio is $A^2$, the same definition gives $10{\log }_{10}(A^2)=20{\log }_{10}A$. Contrast also needs a delay or time range: an optical prepulse, an optical postpulse and a long optical pulse pedestal can have the same relative height but different positions and laser pulse energies. The pedestal energy fraction additionally requires integration over the contribution's duration.

A useful nonlinear measurement is third-order intensity autocorrelation. In an ideal instantaneous model, an input light intensity $I(t)$ generates a second-harmonic gate proportional to $I^2(t)$. Sum-frequency generation with a delayed fundamental replica gives a recorded signal proportional toThe instrument measures this cross-correlation, rather than simply reading $I(\tau )$. Finite gate width, phase matching, spatial overlap and detector response enter the interpretation.

The1998/99 instrument of J. Collier and colleagues used second-harmonic generation, a Wollaston prism and an optical biprism to form crossing fundamental and harmonic beams. A second crystal generated the sum-frequency signal, imaged through optical filters onto a charge-coupled device. Position encoded delay. An inserted glass etalon produced a delayed replica near $1.5\times 10^{-3}$ of the main signal, recorded on one side of the correlation peak. Figure4 combines window settings shifted with etalons.^[ref]

An independent ideal calculation explains both the asymmetry and a possible third-order pulse correlation ghost. Let $I(t)=g(t)+\epsilon g(t-d)$ represent two identical-shape pulses with well-separated supports and correlation lobes, with the second weaker and delayed. Squaring introduces no overlap term. If $A_g(\tau )=\int g^2(t)g(t+\tau )dt$, expansion givesThe delayed replica produces a lobe of relative order $\epsilon$, while the opposite-delay ghost has order ${\epsilon }^2$. For $\epsilon =0.01$, the scales are about $10^{-2}$ and $10^{-4}$ respectively. These values are predictions of the stated ideal model. Assigning every small correlation feature directly to a separate input pulse would miss this distinction.

A nondetection below the measurement floor establishes a bound under a detection model, rather than demonstrating that no light exists there. Finite dynamic range, detector baseline subtraction, delay coverage and resolution should accompany a reported contrast trace. The Sequoia manufacturer likewise distinguishes optical temporal resolution from the scan step; making that step smaller does not alone narrow the optical response.^[ref]

A Wollaston prism, named for William Hyde Wollaston, is a polarizing beam splitter formed from two birefringent optical prisms with crossed crystal-axis orientations. The two linear polarization components encounter different effective refractive indices and leave in different directions. Both output beams are retained, with orthogonal linear polarizations. A manufacturer describes approximately equal and opposite deviations and explicitly defines its splitting angle as the full angle between the emerging beams.^[ref]

Calcite and quartz implementations illustrate why material matters. The manufacturer uses cemented calcite elements and optically contacted quartz elements; its quartz designs provide smaller splitting angles because the birefringence is smaller. A prism's material, wavelength and cut therefore belong with a stated angular separation, rather than treating that separation as a universal property of the name.^[ref]

The ideal intensity division follows projection onto the prism's polarization axes. For incident linear polarization at angle $\theta$ to one axis and total optical power $P$, a lossless model givesFor an original2milliwatt beam at $\theta =30^{\circ }$, the outputs carry1.5and0.5milliwatts. Equal powers occur at45degrees; they are not guaranteed for every input. Unpolarized light gives equal average powers in this ideal model. Real transmission loss and unequal detector responses require separate characterization.

For an original geometric example, suppose a particular prism produces a symmetric full separation $\Delta =1^{\circ }$. At distance $L=0.50\mathrm{m}$ from a common effective exit point, the separation of beam centres isUsing $\tan \Delta$ for each beam would mistakenly treat the full splitting angle as a one-sided deviation. Finite beam diameters and any exit-face displacement also affect detector placement.

A bench demonstration rotates a polarizer before the Wollaston prism while recording both output powers. Their complementary variation tests the polarization decomposition. An analyzing polarizer after each exit can check the two output directions independently. Unlike the virtual copies produced by an optical biprism, orthogonally polarized beams have no mutual intensity cross term on a polarization-insensitive screen. Projecting coherent beams onto a common polarization can permit interference after suitable spatial overlap; changing direction alone does not supply that projection.