Workplace Illumination – Part 19: Measurements, Calculations, and Simulations

            Assessments of a lighting system installation is necessary to determine its compatibility with shifting or evolving requirements.  A lighting system can be evaluated by direct measurement, calculation of theoretical values, or simulation of the space in software.  Each has its strengths and weaknesses; the choice of method to be employed depends on the status of the installation, objectives of the assessment, and available resources.
            This installment of the series provides an introduction to each type of assessment.  These methods are not mutually exclusive; the most useful evaluation may be obtained by blending methods.  The presentation of concepts is kept brief to maintain a manageable scope in the series.

Measurements
            A formalized program of in-situ illuminance measurements is called a lighting survey.  A lighting survey should be conducted on a “stable” lighting system.  For this purpose, stable is defined as having at least 100 hours of run time and in thermal equilibrium.  Measurements are less reliable if taken too soon after system installation or immediately after switching on the lights.  A color- and cosine-corrected illuminance meter should be used to duplicate, as closely as possible, human perception of light.
            The number and location of measurement points are defined by establishing a survey grid.  One method of determining an appropriate survey grid involves calculation of the room index (RI):

where l and w are the length and width of the area (m), respectively and h is the mounting height (m) of luminaires above the workplane (commonly accepted as 0.85 m above the floor).
            From room index, the parameter x is derived by rounding RI up to the next integer value, with a maximum value of 4.  The minimum number of measurement points needed is found as (x + 2)^2.  Given that x is always an integer value in the range 1 – 4, the minimum number of measurement points is always 9, 16, 25, or 36.  The measurement points are distributed throughout the space with consistent spacing in each dimension.  It is also advantageous to use similar spacing in both dimensions.
            An alternate method of grid determination involves calculation of maximum measurement point spacing:  p = 0.2 ⋅ 5^log l, where p is the maximum distance between measurement points (m) and l is the length (i.e. larger dimension) of the survey space (m).  Dividing l by p and rounding the result up to the next integer value gives the number of measurement points needed along the length of the space.  Repeating this for the width yields similar spacing in both dimensions.
            It is customary to place measurement points near the perimeter at one-half (1/2) the spacing distance from the edge of the survey area.  A 0.5 m-wide area along walls that border a survey space can be excluded from the survey area if no part of a task area resides within it.  Irregularly-shaped spaces can be divided into rectangular areas and remainders that approximate rectangles, each with its own survey grid.
 
            For each survey, descriptive information should be recorded to establish the context of the assessment, including:

• Motivation for conducting the survey (e.g. complaint, changes in facility layout or task requirements, etc.)
• Name of person(s) conducting the survey, recording data, etc.
• Definition of the survey area.  For small, simple survey areas, a verbal description may suffice; however, a diagram locating the survey area within the greater facility is advantageous.
• Age of luminaires, lamps, ballasts, control gear, and any other relevant system components.
• Condition of luminaires, lamps, etc., such as physical damage, cleanliness, and material degradation (e.g. hazing of diffusers).
• Measurement equipment information, including model and calibration data.
• Notes pertaining to the assessment, including relevant observations (e.g. abnormal air quality, flicker, unplanned task lighting, etc.) and details of deviations from the survey plan.
• Input from occupants of the space, including subjective assessments of lighting quality and visual performance.

            At the time of each measurement, additional information should be recorded, including:

• Date and time of measurement.
• Identification of measurement point.  An alphanumeric row-column identification scheme displayed on a survey grid diagram simplifies measurement point referencing.  A diagram also provides a convenient format on which to display survey results, while an alphanumeric scheme clearly identifies tabulated data.
• Deviations from planned grid position or measurement height required by obstructions (e.g. machinery).
• Illuminance measured by meter.
• Ambient temperature; temperature of lamp or luminaire is also useful, if it can be obtained.
• Voltage applied to luminaires and quality of electrical supply, if appropriate resources are available to safely acquire this information.

            For a daylit space, additional steps are required to determine the contributions of daylight and artificial light to measured illuminance.  Using the survey grid defined above, the procedure is as follows:

1. Measure the daylight illuminance in an exterior location unaffected by artificial light.
2. With artificial lighting switched off, measure illuminance at each survey grid point.
   
3. Calculate the daylight factor (DF) for each survey grid point:
   

  4.  Switch on artificial light and allow it to stabilize (minimum 15 minutes).
  5.  Measure total illuminance at each survey grid point and daylight (exterior) illuminance.
  6. Calculate the contributions of daylight and artificial light to interior illuminances as follows:
        a.  Multiply the exterior illuminance (step 5) by the daylight factor (step 3) to obtain the contribution of daylight to interior illuminance at each survey grid point.
        b.  Subtract the daylight contribution (step 6a) from total interior illuminance (step 5) to obtain the contribution of artificial lighting to interior illuminance at each survey grid point.     Note that the interior and exterior measurements must be “approximately simultaneous;” that is, separated by only a very short period of time (e.g. a few minutes).  Highly variable sky conditions, such as intermittent cloud cover, can also invalidate these measurements.
            If the survey is concerned only with the lighting system’s ability to provide adequate illumination in the worst case, i.e. with no assistance from daylight, measurements can be taken at night.  This eliminates the daylight contribution calculations and expedites completion of the survey.  It does not, however, provide a thorough assessment of lighting system performance, including daylight glare concerns, in combined lighting conditions.
            If an average daylight factor (see Part 13) has been determined for the survey space, it can serve as a shortcut.  DFavg can be substituted for individually determined daylight factors, eliminating the simultaneous interior and exterior measurements.  The illuminance values obtained may provide an indication of the lighting system’s sufficiency, but should not be used for specific lighting decisions.  Visual performance and comfort at any workstation can only be assured by location-specific and time-coordinated measurements; that is, a proper lighting survey.

            Multiple surveys may be conducted throughout the lifecycle of a lighting system.  Conducting surveys at different times of day and year provides insight into the variability of daylight contributions and its impact on visual performance, energy consumption, and other metrics.  Surveys can also be used to evaluate the effectiveness of maintenance procedures and to reveal performance trends that improve predictions of maintenance needs or identify potential control strategy improvements.  Cleaning and relamping schedules can be adjusted accordingly to reduce unjustified cost or improve system performance.
            Subsequent installations may also benefit from improved estimates of maintenance and utilization factors.  Survey results should validate design assumptions or be used to revise the models used for lighting system design.  Changes need not be limited to lighting hardware; materials and surface treatments used in a space can also be modified to improve lighting conditions.

            Discussions of lighting and surveys are often dominated by concerns of illuminance.  However, luminances in the workspace are also important and can be directly measured.  Doing so ensures appropriate luminance contrasts are maintained to support visual task performance.  These measurements can reveal the need for maintenance, such as cleaning or painting of surfaces.  Changes in materials or physical layout may also be identified that would improve a space’s lighting conditions, including the occurrence of glare.

Calculations
            Many values pertaining to lighting can be calculated, either as predictions or as determinations of system performance.  Efficacy, contrast, and uniformity and diversity ratios (see Part 14) have been discussed in previous installments of this series.  Calculations required to design effective daylighting were discussed in Part 13.  Many others may also be needed, depending on the type of source, application, and objectives.
            Exposures to UV, IR, and laser emissions and associated risk factors can be calculated.  As these are somewhat limited in application, exposure calculations are not presented here.  ACGIH provides guidance on these calculations and exposure limits in its “TLVs for Physical Agents;” this or other relevant regulatory documentation should be consulted when managing applicable operations.
            A sample of other calculations is provided as an introduction to the array of available assessment tools.  Control of glare is a critical function of lighting system design.  Effectiveness of glare-control efforts in indoor applications can be evaluated using the Visual Comfort Probability (VCP) or Unified Glare Rating (UGR).

Visual Comfort Probability (VCP)
            VCP predicts the proportion of an observer population that will deem a lighting installation acceptable, comfortable, or unobjectionable.  To facilitate reliable comparisons, luminaires are evaluated under standard conditions:

• 1000 lx (100 fc) initial illuminance.
• 80% ceiling cavity, 50% wall, and 20% floor cavity reflectances (see “Zonal Cavity Method” below).
• Luminaire mounting heights of 2.6 m (8.5 ft), 3 m (10 ft), 4 m (13 ft), and 4.9 m (16 ft) above the floor.
• Square, long-narrow, and short-wide room configurations.
• Uniform distribution of luminaires in the survey space.
• Observation point located 1.2 m (4 ft) in front of the center of the rear wall of the space and 1.2 m (4 ft) above the floor.
• Horizontal line of sight, directly forward.
• Field of view limited to 53° above and directly forward of the observation point.

            To determine VCP, a series of intermediate calculations is required for each luminaire in the survey space.  First, the position index (P) is calculated with the formula
P = exp[(35.2 – 0.31889 α – 1.22 e^(-2α/9))⋅10^-3 ⋅ β + (21 + 0.26667 α – 0.0029663 α^2)⋅10^-5 ⋅ β^2], where α is the angle (degrees) from vertical of a plane containing the source (luminaire) and the line of sight and β is the angle (degrees) between the line of sight and a line connecting the observer and the source.  These angles are depicted in Exhibit 1.

            Next, the average luminance of the field of view, LFOV, is calculated:
LFOV = [Lw ⋅ ωw + Lf ⋅ ωf + Lc ⋅ ωc + ∑( Ls ⋅ ωs)]/5, where L is the average luminance (cd/m2), ω is the solid angle (sr) subtended at the observer, and the subscripts refer to walls (w), floor (f), ceiling (c), and source (s).  This approximation assumes that the entire field of view subtends 5 sr in standard conditions; hence the division by five to obtain the average.
            The next step is to calculate the function Q for each luminaire:
Q = 20.4 ωs + 1.52 ωs^0.2 – 0.075.  Using the values defined above, an index of sensation, M, is calculated:

The index of sensation is then used to calculate a discomfort glare rating (DGR) for the entire field of view: 

where n is the number of sources in the field of view.
            Finally, VCP is calculated:

Fortunately, VCP can also be estimated using the plot of DGR vs VCP shown in Exhibit 2.  VCP data for luminaires tested in standard conditions are often tabulated as shown in Exhibit 3 for rapid reference by system designers.  VCP ≥ 70 is a typical threshold of acceptability.

            The system of VCP calculations has only been validated with lensed direct fluorescent luminaires.  Its limited scope of validation requires an alternative assessment for many applications.  Enter the Unified Glare Rating (UGR).

Unified Glare Rating (UGR)
            CIE developed the Unified Glare Rating (UGR) to provide consistent evaluations across luminaire types, locations, and other installation parameters.  The basic UGR formula is

where Lb is the luminance (cd/m^2) of the field of view less that of the luminaire, L is the luminance (cd/m^2) of the luminaire in the observer’s direction, ω is the solid angle (sr) subtended by the luminaire, and P is the position index of the luminaire, calculated as in the VCP system.  Large luminaires can be subdivided into areas treatable as point sources, as discussed in Part 12, to improve calculation accuracy.
            While UGR is broadly applicable, it, too, has limitations; it is to be used only in situations where 0.0003 ≤ ω ≤ 0.1.  The method can also be modified to use installation-specific parameters (“application-based”) in lieu of the standardized arrangement (“tabular method”).
            UGR values are correlated with subjective assessments of lighting conditions.  Values of 10 or less correspond to imperceptible glare, while values of 28 or higher correspond to uncomfortable conditions.  Several intermediate values along a continuum are also described, as shown in Exhibit 4.  If the VCP of an installation is known, its UGR can be estimated using the curve in Exhibit 5.

            CIE has developed a similar system for outdoor lighting applications.  The Glare Rating (GR) is based on observation of an array of points from a single location.  GR is often used to evaluate sports complexes and is highly dependent upon the observation point chosen.  These characteristics limit its utility in the context of workplaces and, therefore, a detailed discussion is foregone.

Zonal Cavity Method
            The zonal cavity method is used to account for differences between workplane height and the floor and between ceiling height and luminaire mounting height in illuminance calculations.  In this method, a space is divided into three cavities, as depicted in Exhibit 6.  The ceiling cavity consists of the space between the ceiling and the plane of luminaires.  The room cavity contains the space between the plane of luminaires and the workplane.  The floor cavity consists of the space between the workplane and the floor.

            The height of these cavities, identified as hCC, hRC, and hFC, respectively, are used to calculate cavity ratios: 

where h is replaced with hCC, hRC, and hFC to calculate the ceiling cavity ratio (CCR), room cavity ratio (RCR), and floor cavity ratio (FCR), respectively.  The length and width are assumed to be the same in each cavity; therefore, l and w are used without subscripts.  The CR formula above assumes a regularly-shaped (i.e. rectangular) space.  For an irregularly-shaped (i.e. non-rectangular) space,

            Calculated cavity ratios and known room surface reflectances are used to determine effective cavity reflectances.  Effective cavity reflectances replace surface, or base, reflectances in determinations of luminance ratios, etc.  Exhibit 7 shows the look-up table for base reflectances of 50 – 90%.  Note that when CR = 0, the effective cavity reflectance equals the base reflectance.  For example, surface-mount or recessed lighting creates a zero-height ceiling cavity and, therefore, CCR = 0.  Thus, the ceiling (i.e. base) reflectance is the cavity reflectance.

Cubic Illuminance
            The use of vector algebra in its calculations places a thorough discussion of cubic illuminance outside the scope of this series.  Nonetheless, an introduction to the concept is useful, as it facilitates visualization of some practical concerns of lighting installations.
            Consider a cube of infinitesimal size, centered at a point of interest, such as the center of a workstation or other task area.  The cube’s surfaces are aligned with the coordinate system used to define the space.  Each face of the cube receives optical radiation according to the lighting conditions of its surroundings, defined by opposing pairs of illuminances.  For simplicity, these can be called the left/right, top/bottom, and front/rear pairs.
            Continuing to consider cubic illuminance only in conceptual terms, each pair of facial illuminances affects visual performance in its own way.  For purposes of this presentation, it is assumed that a person working in the hypothetical task area is positioned on the “front” side of the cube.  In this scenario, the front/back illuminance pair represents the potential for shadowing of the task area by the operator (front illuminance) and for glare (rear illuminance).
            Similarly, the top/bottom pair represents the contrast of the task area.  That is, illuminance from below must be in service of the visual task performed (e.g. intentional backlighting) or be counteracted by illuminance from above to maintain visual performance and comfort.
            If at similar levels, the left/right pair are nearly independent of each other, illuminating the activity of each hand, for example.  If the levels are significantly different, however, shadows on one side and/or glare on the other can limit visual performance and comfort.
            Without the calculation procedure delineated, cubic illuminance provides a useful aid to workspace planning.  The orientation of workspaces and the placement of equipment and materials relative to a lighting system can be effectively guided by this model, even if only qualitatively.

     Numerous calculations are relevant to lighting system design and evaluation.  Any attempt to represent the full range quickly becomes unwieldy in a presentation of this type.  In this series, only a sample can be provided; the references cited, and other resources, provide much more expansive presentations for those interested in diving deeper.

Simulations
            Software becomes ever-more versatile as computing power increases and the cost to obtain it decreases.  Several available tools are capable of accepting application-specific information, including three-dimensional models of planned spaces.  Luminaire information can also be loaded directly from many manufacturers’ databases, ensuring models are based on accurate information.
            Various types of output can be obtained, including 2D (plan view or elevation) illuminance maps and 3D renderings of entire spaces.  Very detailed 3D representations are possible, with high degrees of accuracy, when all contents of a space are included in the model input.  A large amount of data is required for the most accurate renderings; these can be computationally intensive.  However, the confidence gained in the long-term performance expectations of a lighting system can justify the proactive investment.
            Perhaps most impressive is that many of these powerful tools can be utilized free of charge.  Some are created by individual manufacturers and are, therefore, limited to analysis of their own products.  Others are subsidized by large consortia of manufacturers, vastly increasing the options available in a model.   None are named here, lest it be construed as an endorsement; these tools must be evaluated with respect to a project and the abilities of team members to use them effectively.


            For additional guidance or assistance with Safety, Health, and Environmental (SHE) issues, or other Operations challenges, feel free to leave a comment, contact JayWink Solutions, or schedule an appointment.

            For a directory of “Workplace Illumination” volumes on “The Third Degree,” see Part 1:  An Introduction to Lighting (21Aug2024).

References
[Link] “Computing Visual Comfort Ratings For a Specific Interior Lighting Installation.”  Sylvester K. Guth.  Illuminating Engineering; October 1966.
[Link] “Cubic illumination.”  C. Cuttle.  International Journal of Lighting Research and Technology; January 1997.
[Link] Lighting for Health and Safety.  N.A. Smith.  Butterworth-Heinemann; 2000.
[Link] The IESNA Lighting Handbook, 9ed.  Mark S. Rea (ed).  Illuminating Engineering Society of North America; 2000.
[Link] Lighting Engineering:  Applied calculations.  R. H. Simons and A. R. Bean.  Butterworth-Heinemann; 2001.
[Link] Energy efficiency in buildings:  CIBSE Guide F, 3ed.  The Chartered Institution of Building Services Engineers; May 2012.
[Link] Handbook of Human Factors and Ergonomics, 4ed.  Gavriel Salvendy (ed).  John Wiley and Sons; 2012.
[Link] The SLL Code for Lighting.  The Society of Light and Lighting; March 2012.
[Link] “Addressing Glare in Solid‐State Lighting.”  Jeff Shuster.  Cooper Lighting Solutions; January 2014.
[Link]  Digital Transformations for Lighting in the Workplace.  Darina Dupláková and  Ján Duplák.  CRC Press, 2023.
[Link] “Threshold Limit Values for Chemical Substances and Physical Agents.”  American Conference of Governmental Industrial Hygienists (ACGIH); latest edition.

Jody W. Phelps, MSc, PMP®, MBA
Principal Consultant
JayWink Solutions, LLC
[email protected]