## 1 Introduction  
The development of micro-nano technologies, integrated microfluidic systems has emerged as a widely used scheme for \"lab on a chip\" device miniaturization. Such systems have been used in various medical and chemical applications, e.g., chemical analysis and synthesis, two-phase mixing, and particle sorting [1; 2; 3]. Many of these topics, such as flow cytometry, particle counting, and droplet generation, require the accurate measurement and control of flow rate within the microfluidic channels [4; 5; 6; 7]. Thus, a flowmetry sensor is an essential component in the microfluidic systems.  
Given its own intrinsic advantages, in particular, lowered cost, design simplicity, and high accuracy, optical feedback interferometry (OFI) has drawn great attention in metrology research [8; 9; 10; 11; 12]. In an OFI sensor, a part of the laser radiation is reflected or back-scattered from the distant target, and the back-propagating radiation re-enters the laser cavity where it interferes with the original laser wave. It results in a variation of the laser output power or its junction voltage [13; 14]. In the case of a velocity measurement, the back-scattered wave frequency will be shifted due to the Doppler effect. Thus, the laser power variation will be a periodic function with a frequency \(f_{D}\) that can be expressed as:  
\[f_{D}=\frac{2V\text{-}sin\theta}{\lambda}, \tag{1}\]  
where \(\lambda\) is the laser wavelength, \(V\) is the target velocity, \(\theta\) is the incident angle formed by the laser propagation axis and perpendicular to the channel chip.  
OFI based microfluidic sensors have been reported since the last decade [15]. Using this technique, [PERSON] et al. implemented a flowing velocity profile measurement system. This was done in a polydimethylsiloxane based elastomer (PDMS) microchannel with a 320 \(\upmu\)m internal diameter, thereby achieving a clear and outstanding Doppler spectral peak in the signal spectra [16]. [PERSON] et al. enabled the velocity profile measurement of milk-oil two-phase flow in a Y-shaped microchannel [17]. In a previous publication, the authors had demonstrated a reasonable OFI based on a flowmetry spectral signal in a \(100\times 100\)\(\upmu\)m square microchannel [18]. However, in the existing sensing systems, the optical configurations were bulk and suffered from a delicate alignment of free-space optics to couple the laser beam to the microchannel. Thus, a miniaturized OFI sensing system without the bulk optics, that can be integrated with the microchannel, is preferable. [PERSON] et al. [19], for the first time, facilitated the miniaturization of the OFI sensor using an optical fiber coupling inside the channel chip and achieved reasonable measurement results. However, in their work, the signal level was considerably lower than the standard bulk configuration, where a maximum 15 dB signal-to-noise ratio (SNR) was reached. Therefore, sensitive and robust integrated OFI flowing sensor systems are still required.  
In this work, based on the use of the vertical-cavity surface-emitting lasers (VCSELs), we proposed the design of a micro-scale OFI flowmetry sensor system by integrating micro-optical elements directly on the top surface of the VCSEL chip and on the microchannel surface. We describe the fabrication process, discuss the technological constraints that were addressed, and present a set of results that highlight the experimental performances of our novel home-made system. The paper is constructed as follows: first, the fabrication procedure of the micro-scale component (lens on laser and microfluidic channel) is described in detail. Second, the electronic and optical characteristics are investigated to analyze the laser output performance. Finally, the flowmetry measurement is performed using this new compact system. The results are compared with the ones obtained using a traditional bulk glass lens pair to investigate the system sensitivity.