LESSON 09 / About 30 min

One light wave, three linked quantities.

Wavelength, Frequency & Energy

Connect space, time and photon energy; then test how a medium, an optical power setting and an objective change the comparison.

Before you begin

Resolution & Numerical Aperture · Detectors, Noise & Exposure

Try a setting, save an observation, then change one thing. The explanation checks are optional.

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Lesson outline
  1. Space and time describe the same wave

    Wavelength is a distance between repeating phases. Frequency counts cycles per second at one place. A traveling wave connects them through speed = wavelength × frequency.

    Wavelength counts space; frequency counts time. Know the propagation speed before converting between them.

  2. Enter a stationary transparent medium

    At a stationary interface, transmitted light keeps the source frequency. Its phase speed and wavelength change together.

    Specify whether a wavelength is in vacuum or in a medium. A shorter in-medium wavelength does not mean a higher-frequency photon.

  3. Energy per photon is not beam power

    The quantum relation E = hf assigns an energy to each photon of a monochromatic beam. Optical power measures the energy delivered per second by the whole beam.

    Always name the comparison: energy per photon, photons per second, or energy over an exposure.

  4. Decide what “equal light” means

    Equal watts and equal photon rates are different comparisons across wavelengths. Select the quantity to hold fixed before interpreting a camera signal.

    Make “equal” explicit. A power-normalized comparison is not automatically a photon-normalized comparison.

  5. A shorter wavelength is a tradeoff

    Shorter imaging wavelengths reduce an ideal diffraction length at fixed NA. That calculation alone cannot predict useful image quality or biological damage.

    Use wavelength to calculate a defined optical limit, then evaluate the experiment’s photon budget and specimen response separately.

Model, limits & sources

All wavelength controls specify vacuum wavelength λ₀. Frequencies and photon energies use exact SI constants; displayed values are rounded. Refractive index is selected independently and describes phase velocity in a transparent, linear, stationary medium.

The spatial and temporal traces are field components with arbitrary amplitude, not photon trajectories. Boundary drawings omit reflected light, absorption, polarization and amplitude transmission coefficients.

The optical power ledger assumes a monochromatic beam and steady illumination. Absorption is an independent illustrative fraction, not a material spectrum or a biological damage model.

The Airy cross-section assumes an aberration-free circular pupil and incoherent point imaging. Its normalized intensity is calculated from [2 J₁(u)/u]², with u = 2π NA r/λ₀. Sampling and noise are not included in that curve. NA values above one require an appropriate immersion system.

Read further

PUT THE IDEA TO WORK

Convert incident photon counts to electrons, then account for noise, camera limits and digitization.

Follow those photons into a detector ↗

Experiment, enlarged