Analytical assessment of the photon exposure

Although UVC radiation spans a spectrum of wavelengths ranging from approximately 0.01 – 0.40 µm, the most readily available bulbs emit at the 0.254 µm wavelength. It should be noted that there are other wavelengths that are known to be effective (i.e., strongly absorbed) such as 0.222 µm9 since DNA molecules will absorb radiation up to a maximum wavelength of 260 nm10. Thus, the energy associated with photons of the 0.254 µm wavelength can readily be determined using the simple relation developed by Max Planck below relating the photon energy to the frequency11.

$$E = hnu = hfracclambda = left( 6.1260693*10^ – 34 ;textJ;texts right)left[ {frac3.0*10^8 ;textm/s2.54*10^ – 7 ;textm} right] = 7.236*10^ – 19 ;textJ;textper;textphoton$$

To determine the exposure, one ultimately needs the number of photons emitted per second from the UV source (a fluorescent bulb in our case). Since each bulb used was rated to emit 48 watts (W) of UVC light, and 1 W equals 1 J per second, one can divide this by the energy of each photon to get the total source strength, (S).

$$S = frac48;textJ/s7.236*10^ – 19 ;textJ/photon = 6.634*10^19 ;textphotons/s$$

Although we now have the total number of photons emitted, we must account for the geometry of the source (bulb) as well as the geometric orientation between the source and the targets (masks) to determine the number of photons that will actually strike the masks and become absorbed (deposit energy). This is shown schematically in Fig. 1. Each bulb measures 5-ft long and is therefore best approximated as a finite line source. If we assume that the UV light emitted from each bulb is isotropic or equal in all directions, then we can use the equation below to yield the number of photons that would strike a target (mask) at some distance (x) away[11, p. 340].

$$phi = fracS_l 4pi xleft[ {tan^ – 1 left( fracl_2 x right) + tan^ – 1 left( fracl_1 x right)} right] to fractextphotonstextcm^2 ;texts$$

Figure 1

Approximate geometric orientation between the UV bulbs and masks.

In the equation above, (S_l) is simply the source strength, (S), divided by the total length of the bulb, (l). This flux quantity, (phi), is then determined by assuming that the masks to be irradiated lie along the midplane of the bulbs and that the distance between the bulbs and masks is 8 ft, which is the rough midpoint distance in the sterilization room. Dividing this quantity by the energy of each photon that was previously determined will yield the units of exposure that we desire.

$$textexposure = fracphi E to fractextmJtextcm^2 $$

For a single bulb that measures 5-ft long rated at 48 W, it will take approximately 16 min to achieve the desired exposure goal of 60 mJ/cm2 if the mask is placed 8-ft away along the bulb centerline. If two additional bulbs are accounted for at distances of 10-ft and 12-ft from the mask, the irradiation time drops to about 7.65 min.

Room layout and experimental measurements of the photon exposure

A total of twelve 5-ft long bulbs were placed around the sterilization room as shown in Fig. 2. Four bulbs are on the front wall with door, four bulbs are on the back wall, two bulbs are on the ceiling, and one bulb each is on the remaining walls. All walls have been covered with standard aluminum foil due to the highly reflective property of this material, and masks were strung across the x-direction as shown in Fig. 3. The x-direction measures approximately 22 ft, the y-direction 14 ft, and the floor-to-ceiling is 10 ft.

Figure 2
figure 2

A top-down (left) and isometric (right) view of the UV sterilization room with bulb placements.

Figure 3
figure 3

Picture taken of the sterilization room at hospital. The walls are covered with aluminum foil, and facemasks are strung on several different lines across the room.

The centerline distance in the y-direction is approximately 7 ft (a conservative value of 8 ft was used in the analytical calculation). The lines were strung such that some of the lines/masks were closer to the front wall while others were by default closer to the back wall, but the masks were spaced to ensure that there was no shadowing. Before any masks were hung on the lines and irradiated, a photometer (model PMA2100; Solar Light Company, LLC) was used to measure the exposure in the sterilization room at nine different locations (designated with the stars in Fig. 2). The photometer was connected to a germicidal UVC detector (model PMA2122-WP; Solar Light Company, LLC) which has a range of 0–2000 µW/cm2 and a sensitivity to 254 nm wavelength, and both devices came with certificates of calibration12. These locations encompassed the limiting positions where masks would be placed, and two measurements were taken at each location. For one measurement the photometer window would face the front wall, and for the second measurement the photometer would face the back wall. This would ensure that both sides of the masks were receiving the necessary exposure, since the UVC radiation will not penetrate from one side of a mask through to the other side.

All measurements were taken by an individual wearing proper protective equipment. The individual would hold the photometer in position until the readout stabilized, and these values were recorded. The photometer readout is given in units of micro watts per cm2, an energy rate, but this can easily be converted into mJ/cm2, total energy. The minimum measurement was 100 µW/cm2, and this was observed at the position designated with the purple star in Fig. 2 with the photometer window facing the door. With an energy deposition rate of 100 µW/cm2, it will take 10 min to reach the exposure goal of 60 mJ/cm2. Since all other position readings were significantly larger than this, with a maximum of 300 µW/cm2, all mask positions were ensured to receive the appropriate exposure over a 10-min irradiation time. In fact, the three-bulb analytical solution of 7.65 min calculated above corresponds to a photometer reading of about 130 µW/cm2, which again, validates the chosen 10-min irradiation time.

Simulation results

Visual Lighting 2017 by Acuity Brands13 was used to simulate the light distribution inside the UV sterilization room. Visual is a software simulation tool commonly used in the commercial lighting design industry that enables the simulation of light reflectance and transmittance in a three-dimensional environment. The tool calculates lighting power density on various surfaces and the lighting transmittance through a plane. To perform the calculations, a model was developed to match the physical environment accounting both for the actual dimensions and the added reflectivity due to the aluminum foil on the walls. Lighting fixtures, or luminaires, are simulated using industry-standard .IES files. These files simulate the lighting lumen output and ray distribution unique to a particular luminaire. The actual lights used are Phillips TUV 64T5 HO 4P SE UNP/32. As these are bare lamps and not part of a specific luminaire, no IES file was available. Thus, an IES file for a single-lamp fluorescent luminaire was used, and the lumen output was adjusted to match the output of the Phillips lamps. Results are shown schematically in Fig. 4 with the reflectivity of the walls and ceiling set to 50%. This conservative value was chosen since the transmissivity of opaque solids is generally zero[3, p. 769] and the absorptivity of aluminum foil is approximately 0.15[3, p. 777]. Thus, the actual reflectivity of aluminum foil is closer to 85%.

Figure 4
figure 4

UV power density on the floor (left) and through a vertical plane spanning the center of the room (right).

The software natively performs calculations in foot-candles (fc) or lux (lx), and one fc is equal to approximately 1.57 µW/cm2. Thus, the minimum photometer reading of 100 µW/cm2 corresponds to 63.7 fc. As can be seen in Fig. 4 (left picture), the entire volume of the room encompassing the masks is subjected to well over 100 fc as designated with the yellow, orange, and red coloration. The red coloration in the right picture verifies that the masks located at the y-direction midplane receive upwards of 290 fc, which again validates that the masks will receive an exposure well above the minimum goal of 60 mJ/cm2.