Streak Camera
Temporal resolution of a streak camera: the slit image, one pixel and screen blur (lengths converted to time by the sweep speed), the tube's own spread and trigger jitter, convolved; and the time window on the screen.
Slit-Image Term
176.059 fs
w·M / v
Pixel Term
61.970 fs
p / v (time per pixel)
Temporal Resolution (FWHM)
692.280 fs
Rectangles ⊗ Gaussian; the tube, blur and jitter term dominates. Quadrature would give 705.538 fs
Screen Blur Term
461.461 fs
72.6 µm FWHM on the screen: 35 lp/mm read as 5 % MTF, times M
Tube Spread the Data Sheet Allows
640.938 fs
Largest Gaussian tube term that keeps the total at 800.000 fs with these slit, pixel, blur and jitter terms; valid at the sweep the spec was measured at (C16910: fastest), and it also holds the test pulse width
Time Window
59.987 ps
968 pixels × p / v (inside the 18 mm screen)
Key Formulas
Δtslit = wslit·M / vsweep; Δtpixel = p / vsweep
Gaussian terms: ΔtG = √(Δttube² + Δtjitter² + (b/v)²) (Gaussians add in quadrature)
Δt = FWHM of rect(Δtslit) ⊗ rect(Δtpixel) ⊗ Gauss(ΔtG); no Gaussian: max(Δtslit, Δtpixel)
Twindow = min(Npixels·p, Lscreen) / vsweep; a FWHM below 2p/v is undersampled
Blur: Gaussian MTF exp(−2π²σ²f²) = 5 % at the limiting resolution f, FWHM = 2.3548·√(ln 20 / 2)/(π f) at the cathode (26.2 µm at 35 lp/mm), times M on the screen
Tube spread: the tube's own Gaussian term, chiefly transit-time dispersion from the photoelectron energy spread, ≈ 2.63·√Δε / E ps (Δε FWHM of the photoelectron energy distribution in eV, extraction field E in kV/mm; Shakya & Chang 2005 after Chang et al. 1996), plus deflection dispersion. The delay between electrons leaving the cathode with 0 and with Δε, √(2m_eΔε)/(eE) = 3.37·√Δε / E ps, bounds it from above. A data-sheet resolution includes the slit and readout, so it bounds the tube term from above.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Slit image and pixel are rectangles, tube, blur and jitter Gaussians; exact FWHM of their convolution. Blur: 5 % Gaussian MTF at the cathode limit, × M. Trigger jitter is entered as FWHM. Defaults: C16910, 60 ps sweep.
- Hamamatsu Photonics (2008). Guide to Streak Cameras, cat. no. SHSS0006E. Temporal resolution as the FWHM of the streak image of a delta pulse; trigger jitter in summed sweeps. hamamatsu.com
- Hamamatsu Photonics. Streak camera C16910 data sheet, cat. no. SHSS0026E06: temporal resolution < 800 fs, Ø18 mm P-43 phosphor screen, 35 lp/mm at the photocathode centre, effective photocathode 0.15 × 4.5 mm and working area 12.48 × 9.44 mm (1280 × 968 pixels) with an ORCA-Flash4.0 V3 behind 3:2 output optics, 1:1 input optics, fastest sweep ≈ 60 ps per full screen. hamamatsu.com
- Zavoisky E. K., Fanchenko S. D. (1965). Image converter high-speed photography with 10⁻⁹–10⁻¹⁴ sec time resolution. Appl. Opt. 4, 1155–1167. Technical (slit image/sweep speed) and physical (energy spread) limits of the time resolution. doi:10.1364/AO.4.001155
- Shakya M. M., Chang Z. (2005). Achieving 280 fs resolution with a streak camera by reducing the deflection dispersion. Appl. Phys. Lett. 87, 041103. Transit-time dispersion 2.63·√Δε/E ps (Δε in eV, E in kV/mm) and deflection dispersion as tube terms. doi:10.1063/1.2001732
- Chang Z., Rundquist A., Zhou J., et al. (1996). Demonstration of a sub-picosecond x-ray streak camera. Appl. Phys. Lett. 69, 133. Source of the 2.63·√Δε/E transit-time estimate. doi:10.1063/1.118099