Inexpensive two-dimensional measuring device for cryogenic temperatures

A profile projector projects a magnified image or profile of a sample onto a screen for comparison to a standard.

Common glass breaks when submerged in liquid nitrogen. A transparent material able to withstand the direct addition of liquid nitrogen is pyrex.

The thermal diffusivity is a measure of the capacity of a material to conduct heat through a medium. Materials with very low thermal diffusivity, such as quartz, transmit heat to neighboring objects very slowly. The images of the sample at 77 K must be scanned quickly before the CCDs cool to this temperature.

The thermal diffusivity $κ$ is defined as $k∕ρcp$⁠, where $k$ is the thermal conductivity, $CP$ the specific heat at constant pressure, and $ρ$ the material density.

In the steady state, the heat flux through the layers between the scanner and the liquid nitrogen is $ϕ≃4.2W(Σ(ai∕ki)≃1.5+0.2+1,150+0.15+28,750=29,901W−1cm2K$⁠; $S=576cm2$⁠; $T1−T6=−221K$⁠).

The energy radiated in the unit of time by the scanner is given by the integral of the spectral radiancy of a blackbody at room temperature $R=SσT4=25W$⁠.

According to Wien’s equation, the wavelength peak for blackbody radiation occurs at $λm[μm]=2890∕T$⁠. If $T=298Kλm=9.7μm$⁠. Because electromagnetic radiation of this wavelength is almost completely absorbed by a glass window of 2 mm thick, the optical sensors and electronic components do not cool by the release of infrared radiation.

A sample is a measurement of tone or color at a given place of a scanned or bitmapped image. The maximum possible value of spi that can be achieved without interpolation is the optical resolution of the scanner. Other nomenclatures are used to define the image resolution depending on the output format. For instance, the term dots per inch (dpi) refers to the resolution of printable images, and pixels per inch (ppi) refers to images displayed on a computer screen. The term lines per inch (lpi) is used to define the halftones of an image that is going to be printed. We suggest the book, D. Blatner, G. Fleishman, and S. Roth, Real World Scanning and Halftones (Peachpit, Berkeley, 1998), for a complete introduction to the world of scanners.

To carry out the two-dimensional analysis of the scanned images, we recommend the software AutoCAD $14.0+$⁠.

The coefficient of thermal expansion $β$ and the heat capacity $CV$ are related by $βVBT=γCV$⁠, where $V$ is the volume of the solid and $γ$ is the Grüneisen parameter defined by $γ=V(∂P∕∂U)V$⁠. Grüneisen’s first approximation is that the parameters $γ$ and $VBT$ are independent of $T$⁠.

The value of $R$ is irrelevant for the calculation of $α$⁠, because it appears in the numerator and denominator of Eq. (7).