# Laser-Driven Light Source Questions and Answers

Energetiq, a subsidiary of Hamamatsu Photonics, manufactures advanced light sources used in complex scientific and engineering applications such as analytical instruments for life sciences and leading-edge semiconductor manufacture.

One of Energetiq’s most successful products is the Laser-Driven Light Source (LDLS™). The LDLS is ideal when used in applications requiring nanoscale areas of illumination – up to 1mm2. This high radiance light source has very high spatial and long-term spectral stability for consistently accurate measurements.

Radiometry is the science of measuring radiation energy in any portion of the electromagnetic spectrum. In practice, the term is usually limited to the measurement of ultraviolet (UV), visible (VIS), and infrared (IR) radiation using optical instruments. Broadband radiation sources emitting UV-VIS-IR wavelength radiation, such as Energetiq’s LDLS, are characterized using radiometry and its units.

The SI unit of radiance is watts per square meter per steradian [W·m-2·sr-1]. Since many radiation sources used in laboratories have emitting area in the square millimeters range, the unit of milliwatts per square millimeter per steradian [mW·mm-2·sr-1] is often used for radiance. As shown in Figure 1, the radiance (R) of the source emitting area (A) equals the radiation power (P), which is emitted from A and propagates in solid angle Ω, divided by the area A and the solid angle Ω: R = P / (A x Ω).

Figure 1. Radiance (R) of source is the Power (P) emitted from the source emitting Area (A) and propagated in the Solid Angle (Ω).

The steradian [sr] is the SI unit for measuring solid angles, defined by the solid angle (Ω) that projects on the surface of a sphere with a radius of r, having an area (A) equal to r2 (Ω = A/r2 = r2/r2 = 1 [sr]). It describes angular spans in three-dimensional space, analogous to the way in which the radian [rad] describes angles in a two-dimensional plane. The total solid angle for a point in space is 4π steradians.

Figure 2. Steradian [sr] is a unit for measuring solid angles (Ω) defined by the solid angle that projects on the surface of a sphere, with a radius of r, having an area of A = r2 (Ω = A/r2 = r2/r2 = 1 [sr]).

The radiance of a source is increased by increasing its emitted power, by making the emitting area of the source smaller, or by emitting the radiation into a smaller solid angle. Strictly speaking, radiance is defined at every point on the emitting surface, as a function of position, and as a function of the angle of observation. Often, as in the example above, we use radiance of a source to mean the radiance averaged over a finite-sized aperture and over some solid angle of interest.

Radiance is a conserved quantity in an optical system so that radiance measured as watts per unit area per unit solid angle incident on a detector will not exceed the radiance at the emitter. In practice, for any bundle of rays mapping an emitter to a detector, the radiance seen at the detector will be diminished by the light which is absorbed along the way or scattered out of the solid angle of the bundle of rays reaching the detector.

Energetiq’s LDLS have ultra-high radiance from their small emitting area (~ 100μm diameter). Radiation from such a high radiance and small emitting area source can be even more efficiently coupled into systems with small apertures and a limited accepting solid angle—optical systems with small ‘étendue’—such as the narrow slits of a monochromator. (For further discussion of étendue, see Energetiq’s tech note, Etendue and Optical Throughput Calculations.)

Irradiance is the radiometry term for the power per unit area of electromagnetic radiation incident on a surface. The SI unit for irradiance is watts per square meter [W/m2], or milliwatts per square millimeter [mW/mm2]. Irradiance is sometimes called “intensity.”

If a point radiation source emits radiation uniformly in all directions and there is no absorption, then the irradiance drops off in proportion to the distance squared from the source, since the total power is constant and it is spread over an area that increases with the distance squared from the radiation source. To compare the irradiance of different sources, one must take into account the distance from the source. A 50cm distance is often used for such measurements.

Irradiance is a useful measure for applications where power must be delivered to large areas. For example, illuminating a classroom or a football field is primarily a question of delivering a certain number of watts per square meter. This can be achieved by using a single high power source. However, since irradiance does not depend on solid angle, multiple sources can be combined, illuminating the walls or the field from different angles.

Radiant flux is radiant energy per unit time, also called radiant power [W, mW, or μW]. The units of radiant flux do not include area or solid angle. Radiant flux is often used to describe the radiation power output of a radiation source, or the radiation power received by an optical instrument. Examples of radiant flux are:

• The radiation power passing through a pinhole
• The radiation power emerging from the optical fiber of a fiber-coupled laser