## 2 Introduction  
Exposure assessment above 10 GHz is typically done by evaluating the power density (PD) at the exposure plane [1; 2], which can be obtained through the electric (\(E\)-) and magnetic (\(H\)-) fields at that plane. Depending on the application, the exposure plane may be very close to the antenna under test (AUT), or further away. To determine the safe operating distance, knowledge about the field in the full volume away from the AUT is required. Such knowledge is also valuable for the research and development of radiating (millimeter-wave) devices. It is usually time-consuming to measure the full volume of interest; however, rather than measuring the full volume, it is possible to reconstruct the electromagnetic field (EMF) from a set of suitable measurements, as the field is constrained by Maxwell's equations. For this purpose, the reliable measurement of both the magnitude and phase of the radiated field is required [3; 4; 5]. However, the development of measurement instruments that capture the varying phase of the quantities becomes more difficult and costly with increasing frequency. As a result, the proper characterization of antennas often relies on phaseless (sometimes referred to as magnitude-only or intensity-only) measurements. Subsequently, the acquired phaseless data are used to reconstruct the phasors through a so-called phase-reconstruction (PR) algorithm. In the pioneering work of [PERSON] [6] and [PERSON] [7], the PR problem was solved using an alternating projection method, also known as the plane-to-plane (PTP) backpropagation method. The proposed method iteratively estimates the missing phases of the measurements at two sufficiently separate surfaces and performs a field propagation between the two scans. The measurement layer (most often a plane) is usually placed at a distance of a few wavelengths from the AUT. Various modifications of the PTP method were later successfully applied for different antenna problems [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. Some usual limitations of the developed procedures include the requirement of a huge number of measurement points (depending on the beam pattern) and limitations on the propagation geometry, which is required to be the same as the measurement surface. Based on these research efforts [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18], commercial systems have been developed to perform PR in the far field. Typical reconstruction algorithms aim at obtaining the \(E\)- and \(H\)- field phasors in the far-field region. Nevertheless, the reactive near field is becoming increasingly important for consumer millimeter-wave devices. The already proposed methods in the literature are limited in terms of reconstructing the reactive components at distances closer than the measurement plane when using backpropagation. This paper presents a forward transformation (FT) approach to reconstruct the EMF in the full half-space above a measurement plane that is placed at a distance of 2 mm from the AUT. The approach leverages the well-known field integral equations [19] and the millimeter-wave probe EUmmWVx [20], which allows measurements of the \(E\)-field very close to the source--i.e., at distances of a fraction of the wavelength--with minimal probe-related distortions of the field at frequencies up to 110 GHz. This property results in a characterization mechanism that only requires few measurements close to the AUT to capture the whole radiated power, thereby reducing the overall computation and measurement cost for the AUT. To obtain the phase information in the near-field region, we employed the phase reconstruction algorithm developed in [21]. The obtained field phasors are used to evaluate the far-field radiation pattern using the expression of the field profile as an equivalent distribution of dipole moments [22; 23; 24].