Key Insights
The Heads-Up Display (HUD) market is experiencing substantial expansion, driven by the increasing demand for advanced driver-assistance systems (ADAS) and enhanced automotive safety features. This growth is propelled by the integration of augmented reality (AR) for more intuitive driving experiences and the rising consumer preference for convenience and safety. Technological advancements in miniaturization and display clarity are further accelerating market development. The market is segmented by HUD type (windshield-based, combiner-based, AR-based) and application (automotive, military, aviation). Geographic expansion, particularly in emerging economies with rising vehicle sales, presents significant opportunities, although high initial investment and integration complexities remain challenges.
Heads Up Display Industry Market Size (In Billion)
The competitive landscape features established automotive component manufacturers and specialized HUD developers. Key players are leveraging their expertise and market presence through strategic partnerships and collaborations to drive innovation. Future growth will be shaped by continuous advancements in display technology, deeper integration with ADAS, and the expansion of HUD applications into consumer electronics and industrial sectors. The Asia-Pacific region is anticipated to show the highest growth rate, fueled by robust automotive production and increasing consumer demand.
Heads Up Display Industry Company Market Share
This report offers an in-depth analysis of the Heads-Up Display (HUD) industry, covering the period from 2019 to 2033, with a base year of 2025. The global Heads Up Display market is projected to reach $6.38 billion by 2033, exhibiting a Compound Annual Growth Rate (CAGR) of 14% during the forecast period. This analysis includes market segmentation, key players, technological trends, and future growth prospects.
Heads Up Display Industry Market Concentration & Innovation
The HUD market is moderately concentrated, with several key players holding significant market share. While exact figures are proprietary, Collins Aerospace, Denso Corporation, and Visteon Corporation are among the leading companies, commanding a combined market share estimated at xx%. Innovation is a crucial driver, fueled by advancements in augmented reality (AR), improved display technologies, and increasing demand for enhanced driver-assistance systems (ADAS). Regulatory frameworks, particularly concerning automotive safety standards, heavily influence product development and adoption. The market also faces competition from substitute technologies, such as advanced infotainment systems with large, high-resolution displays. End-user trends, including a preference for driver convenience and improved safety features, are driving growth. M&A activity within the industry has been moderate, with deal values averaging approximately xx Million in recent years. Notable examples include [Specific examples of M&A activity with deal values if available, otherwise replace with "limited public information"].
- Market Concentration: Moderately concentrated, with top 3 players holding xx% market share (estimated).
- Innovation Drivers: AR technology, improved display technology, ADAS demand.
- Regulatory Impact: Stringent automotive safety standards influence product development.
- Product Substitutes: Advanced infotainment systems.
- End-User Trends: Demand for driver convenience and safety features.
- M&A Activity: Moderate activity, average deal value of xx Million (estimated).
Heads Up Display Industry Industry Trends & Insights
The HUD market is experiencing robust growth, driven primarily by the increasing adoption of ADAS in the automotive sector and the demand for enhanced situational awareness in military and aviation applications. Technological advancements, particularly in AR-HUD, are significantly impacting market dynamics, offering a wider field of view and more immersive user experiences. Consumer preferences are shifting towards seamless integration of HUD systems with vehicle infotainment and navigation systems. The competitive landscape is dynamic, with companies investing heavily in R&D to develop innovative HUD solutions. Market penetration is steadily increasing, particularly in high-income countries, but adoption is growing in emerging economies as well. The overall market exhibits a significant positive growth trajectory. The CAGR for the forecast period (2025-2033) is estimated at xx%, indicating substantial market expansion.
Dominant Markets & Segments in Heads Up Display Industry
The automotive segment dominates the HUD market, accounting for approximately xx% of the total market value. Within the type segment, windshield-based HUDs currently hold the largest market share, followed by combiner-based and AR-based HUDs. AR-based HUDs are expected to witness the highest growth rate in the forecast period due to technological advancements and enhanced user experience.
Dominant Region/Country: North America currently holds the leading position in HUD market share due to the high rate of vehicle production.
Key Drivers (by Segment):
- Automotive: Rising ADAS adoption, increasing vehicle production, stringent safety regulations.
- Military and Civil Aviation: Need for enhanced situational awareness, improved pilot safety, technological advancements in flight navigation systems.
- Other Applications: Growing adoption in maritime navigation, industrial machinery operation, and medical applications.
Dominance Analysis:
North America's dominance is attributed to a high concentration of major automotive manufacturers, a strong regulatory framework promoting safety features, and high consumer spending. However, Asia Pacific is expected to witness significant growth over the forecast period driven by increasing vehicle production and a rising middle class.
Heads Up Display Industry Product Developments
Recent product developments focus on incorporating AR technology to create more intuitive and informative displays. 3D AR-HUDs, with features like wider field of view and improved visibility in all weather conditions, are gaining traction. Key advantages include enhanced safety, improved driver comfort, and seamless integration with other vehicle systems. The market is witnessing a shift towards more compact and energy-efficient HUD designs.
Report Scope & Segmentation Analysis
By Type:
- Windshield-Based Head-Up Display: This segment is currently mature and represents a significant part of the market. Growth in this segment will be driven by improvements in brightness and clarity of the projection.
- Combiner-Based Head-Up Display: This segment is expected to grow moderately, driven by advancements in combiner technology.
- AR-Based Head-Up Display: This segment is expected to exhibit the highest growth rate due to technological advancements and its ability to overlay information on the real world.
By Application:
- Automotive: This segment constitutes the largest share and is predicted to sustain growth due to increasing ADAS adoption.
- Military and Civil Aviation Industry: The demand for increased situational awareness in these sectors will propel growth in this segment.
- Other Applications: While currently smaller, this segment offers opportunities for expansion into diverse fields such as maritime navigation and medical applications.
Each segment includes detailed growth projections, market sizes, and competitive analyses.
Key Drivers of Heads Up Display Industry Growth
The growth of the HUD industry is driven by several key factors: The increasing demand for advanced driver-assistance systems (ADAS) in automobiles, the growing adoption of HUDs in military and aviation applications, and technological advancements leading to more compact, efficient, and feature-rich HUD units. Government regulations mandating safety features in vehicles also contribute to market growth. Moreover, the rising disposable income in developing economies is further fueling the market.
Challenges in the Heads Up Display Industry Sector
The HUD industry faces challenges such as high initial costs of implementation, the complexities of integrating HUD systems with existing vehicle infrastructure, and the potential for supply chain disruptions. Furthermore, intense competition among established and emerging players and the need to meet stringent safety standards add to the challenges.
Emerging Opportunities in Heads Up Display Industry
Emerging opportunities exist in the expansion into new applications such as augmented reality gaming, industrial applications, and even medical contexts. The development of smaller, more energy-efficient HUD systems with enhanced features offers significant market potential. Increased adoption in developing countries with growing vehicle ownership presents further opportunities.
Leading Players in the Heads Up Display Industry Market
- Collins Aerospace (Rockwell Collins Inc)
- Denso Corporation
- Visteon Corporation
- Garmin Ltd
- Thales Group
- BAE Systems PLC
- Nippon Seiki Co Ltd
- Elbit Systems
- Continental AG
- HUDWAY LLC
- Panasonic Automotive Systems (Panasonic Corporation)
- Saab AB
- Pioneer Corporation
Key Developments in Heads Up Display Industry Industry
- June 2021: Hyundai Mobis launches a clusterless HUD for gas and electric vehicles.
- September 2021: Airbus develops an enhanced flight vision system (EFVS) with Collins Aerospace supplying the HUD component.
- January 2022: CY Vision announces automotive 3D AR-HUD with the widest field of view.
Strategic Outlook for Heads Up Display Industry Market
The HUD market is poised for significant growth, driven by technological advancements, increasing adoption in various sectors, and supportive regulatory environments. The integration of AR and AI technologies will further enhance HUD functionality, creating new opportunities for market expansion and innovation. Companies focusing on cost reduction, improved user experience, and seamless integration will be well-positioned for success in this rapidly evolving market.
Heads Up Display Industry Segmentation
-
1. Type
- 1.1. Windshield-Based Head-Up Display
- 1.2. Combiner-Based Head-Up Display
- 1.3. AR-Based Head-Up Display
-
2. Application
- 2.1. Automotive
- 2.2. Military and Civil Aviation Industry
- 2.3. Other Applications
Heads Up Display Industry Segmentation By Geography
-
1. North America
- 1.1. United States
- 1.2. Canada
-
2. Europe
- 2.1. United Kingdom
- 2.2. Germany
- 2.3. France
- 2.4. Rest of Europe
-
3. Asia Pacific
- 3.1. China
- 3.2. Japan
- 3.3. South Korea
- 3.4. Australia
- 3.5. Rest of Asia Pacific
- 4. Rest of the World
Heads Up Display Industry Regional Market Share
Geographic Coverage of Heads Up Display Industry
Heads Up Display Industry REPORT HIGHLIGHTS
| Aspects | Details |
|---|---|
| Study Period | 2020-2034 |
| Base Year | 2025 |
| Estimated Year | 2026 |
| Forecast Period | 2026-2034 |
| Historical Period | 2020-2025 |
| Growth Rate | CAGR of 14% from 2020-2034 |
| Segmentation |
|
Table of Contents
- 1. Introduction
- 1.1. Research Scope
- 1.2. Market Segmentation
- 1.3. Research Methodology
- 1.4. Definitions and Assumptions
- 2. Executive Summary
- 2.1. Introduction
- 3. Market Dynamics
- 3.1. Introduction
- 3.2. Market Drivers
- 3.2.1. Technological Advancements of HUD; Growing Awareness About Passenger and Vehicle Safety
- 3.3. Market Restrains
- 3.3.1. Lack of International Accepted Standards
- 3.4. Market Trends
- 3.4.1. Growing Adoption of HUD in Automotive Industry Driving the Market's Growth
- 4. Market Factor Analysis
- 4.1. Porters Five Forces
- 4.2. Supply/Value Chain
- 4.3. PESTEL analysis
- 4.4. Market Entropy
- 4.5. Patent/Trademark Analysis
- 5. Global Heads Up Display Industry Analysis, Insights and Forecast, 2020-2032
- 5.1. Market Analysis, Insights and Forecast - by Type
- 5.1.1. Windshield-Based Head-Up Display
- 5.1.2. Combiner-Based Head-Up Display
- 5.1.3. AR-Based Head-Up Display
- 5.2. Market Analysis, Insights and Forecast - by Application
- 5.2.1. Automotive
- 5.2.2. Military and Civil Aviation Industry
- 5.2.3. Other Applications
- 5.3. Market Analysis, Insights and Forecast - by Region
- 5.3.1. North America
- 5.3.2. Europe
- 5.3.3. Asia Pacific
- 5.3.4. Rest of the World
- 5.1. Market Analysis, Insights and Forecast - by Type
- 6. North America Heads Up Display Industry Analysis, Insights and Forecast, 2020-2032
- 6.1. Market Analysis, Insights and Forecast - by Type
- 6.1.1. Windshield-Based Head-Up Display
- 6.1.2. Combiner-Based Head-Up Display
- 6.1.3. AR-Based Head-Up Display
- 6.2. Market Analysis, Insights and Forecast - by Application
- 6.2.1. Automotive
- 6.2.2. Military and Civil Aviation Industry
- 6.2.3. Other Applications
- 6.1. Market Analysis, Insights and Forecast - by Type
- 7. Europe Heads Up Display Industry Analysis, Insights and Forecast, 2020-2032
- 7.1. Market Analysis, Insights and Forecast - by Type
- 7.1.1. Windshield-Based Head-Up Display
- 7.1.2. Combiner-Based Head-Up Display
- 7.1.3. AR-Based Head-Up Display
- 7.2. Market Analysis, Insights and Forecast - by Application
- 7.2.1. Automotive
- 7.2.2. Military and Civil Aviation Industry
- 7.2.3. Other Applications
- 7.1. Market Analysis, Insights and Forecast - by Type
- 8. Asia Pacific Heads Up Display Industry Analysis, Insights and Forecast, 2020-2032
- 8.1. Market Analysis, Insights and Forecast - by Type
- 8.1.1. Windshield-Based Head-Up Display
- 8.1.2. Combiner-Based Head-Up Display
- 8.1.3. AR-Based Head-Up Display
- 8.2. Market Analysis, Insights and Forecast - by Application
- 8.2.1. Automotive
- 8.2.2. Military and Civil Aviation Industry
- 8.2.3. Other Applications
- 8.1. Market Analysis, Insights and Forecast - by Type
- 9. Rest of the World Heads Up Display Industry Analysis, Insights and Forecast, 2020-2032
- 9.1. Market Analysis, Insights and Forecast - by Type
- 9.1.1. Windshield-Based Head-Up Display
- 9.1.2. Combiner-Based Head-Up Display
- 9.1.3. AR-Based Head-Up Display
- 9.2. Market Analysis, Insights and Forecast - by Application
- 9.2.1. Automotive
- 9.2.2. Military and Civil Aviation Industry
- 9.2.3. Other Applications
- 9.1. Market Analysis, Insights and Forecast - by Type
- 10. Competitive Analysis
- 10.1. Global Market Share Analysis 2025
- 10.2. Company Profiles
- 10.2.1 Collins Aerospace (Rockwell Collins Inc )
- 10.2.1.1. Overview
- 10.2.1.2. Products
- 10.2.1.3. SWOT Analysis
- 10.2.1.4. Recent Developments
- 10.2.1.5. Financials (Based on Availability)
- 10.2.2 Denso Corporation
- 10.2.2.1. Overview
- 10.2.2.2. Products
- 10.2.2.3. SWOT Analysis
- 10.2.2.4. Recent Developments
- 10.2.2.5. Financials (Based on Availability)
- 10.2.3 Visteon Corporation
- 10.2.3.1. Overview
- 10.2.3.2. Products
- 10.2.3.3. SWOT Analysis
- 10.2.3.4. Recent Developments
- 10.2.3.5. Financials (Based on Availability)
- 10.2.4 Garmin Ltd
- 10.2.4.1. Overview
- 10.2.4.2. Products
- 10.2.4.3. SWOT Analysis
- 10.2.4.4. Recent Developments
- 10.2.4.5. Financials (Based on Availability)
- 10.2.5 Thales Group
- 10.2.5.1. Overview
- 10.2.5.2. Products
- 10.2.5.3. SWOT Analysis
- 10.2.5.4. Recent Developments
- 10.2.5.5. Financials (Based on Availability)
- 10.2.6 BAE Systems PLC
- 10.2.6.1. Overview
- 10.2.6.2. Products
- 10.2.6.3. SWOT Analysis
- 10.2.6.4. Recent Developments
- 10.2.6.5. Financials (Based on Availability)
- 10.2.7 Nippon Seiki Co Ltd
- 10.2.7.1. Overview
- 10.2.7.2. Products
- 10.2.7.3. SWOT Analysis
- 10.2.7.4. Recent Developments
- 10.2.7.5. Financials (Based on Availability)
- 10.2.8 Elbit Systems
- 10.2.8.1. Overview
- 10.2.8.2. Products
- 10.2.8.3. SWOT Analysis
- 10.2.8.4. Recent Developments
- 10.2.8.5. Financials (Based on Availability)
- 10.2.9 Continental AG
- 10.2.9.1. Overview
- 10.2.9.2. Products
- 10.2.9.3. SWOT Analysis
- 10.2.9.4. Recent Developments
- 10.2.9.5. Financials (Based on Availability)
- 10.2.10 HUDWAY LLC
- 10.2.10.1. Overview
- 10.2.10.2. Products
- 10.2.10.3. SWOT Analysis
- 10.2.10.4. Recent Developments
- 10.2.10.5. Financials (Based on Availability)
- 10.2.11 Panasonic Automotive Systems (Panasonic Corporation)
- 10.2.11.1. Overview
- 10.2.11.2. Products
- 10.2.11.3. SWOT Analysis
- 10.2.11.4. Recent Developments
- 10.2.11.5. Financials (Based on Availability)
- 10.2.12 Saab AB
- 10.2.12.1. Overview
- 10.2.12.2. Products
- 10.2.12.3. SWOT Analysis
- 10.2.12.4. Recent Developments
- 10.2.12.5. Financials (Based on Availability)
- 10.2.13 Pioneer Corporation
- 10.2.13.1. Overview
- 10.2.13.2. Products
- 10.2.13.3. SWOT Analysis
- 10.2.13.4. Recent Developments
- 10.2.13.5. Financials (Based on Availability)
- 10.2.1 Collins Aerospace (Rockwell Collins Inc )
List of Figures
- Figure 1: Global Heads Up Display Industry Revenue Breakdown (billion, %) by Region 2025 & 2033
- Figure 2: North America Heads Up Display Industry Revenue (billion), by Type 2025 & 2033
- Figure 3: North America Heads Up Display Industry Revenue Share (%), by Type 2025 & 2033
- Figure 4: North America Heads Up Display Industry Revenue (billion), by Application 2025 & 2033
- Figure 5: North America Heads Up Display Industry Revenue Share (%), by Application 2025 & 2033
- Figure 6: North America Heads Up Display Industry Revenue (billion), by Country 2025 & 2033
- Figure 7: North America Heads Up Display Industry Revenue Share (%), by Country 2025 & 2033
- Figure 8: Europe Heads Up Display Industry Revenue (billion), by Type 2025 & 2033
- Figure 9: Europe Heads Up Display Industry Revenue Share (%), by Type 2025 & 2033
- Figure 10: Europe Heads Up Display Industry Revenue (billion), by Application 2025 & 2033
- Figure 11: Europe Heads Up Display Industry Revenue Share (%), by Application 2025 & 2033
- Figure 12: Europe Heads Up Display Industry Revenue (billion), by Country 2025 & 2033
- Figure 13: Europe Heads Up Display Industry Revenue Share (%), by Country 2025 & 2033
- Figure 14: Asia Pacific Heads Up Display Industry Revenue (billion), by Type 2025 & 2033
- Figure 15: Asia Pacific Heads Up Display Industry Revenue Share (%), by Type 2025 & 2033
- Figure 16: Asia Pacific Heads Up Display Industry Revenue (billion), by Application 2025 & 2033
- Figure 17: Asia Pacific Heads Up Display Industry Revenue Share (%), by Application 2025 & 2033
- Figure 18: Asia Pacific Heads Up Display Industry Revenue (billion), by Country 2025 & 2033
- Figure 19: Asia Pacific Heads Up Display Industry Revenue Share (%), by Country 2025 & 2033
- Figure 20: Rest of the World Heads Up Display Industry Revenue (billion), by Type 2025 & 2033
- Figure 21: Rest of the World Heads Up Display Industry Revenue Share (%), by Type 2025 & 2033
- Figure 22: Rest of the World Heads Up Display Industry Revenue (billion), by Application 2025 & 2033
- Figure 23: Rest of the World Heads Up Display Industry Revenue Share (%), by Application 2025 & 2033
- Figure 24: Rest of the World Heads Up Display Industry Revenue (billion), by Country 2025 & 2033
- Figure 25: Rest of the World Heads Up Display Industry Revenue Share (%), by Country 2025 & 2033
List of Tables
- Table 1: Global Heads Up Display Industry Revenue billion Forecast, by Type 2020 & 2033
- Table 2: Global Heads Up Display Industry Revenue billion Forecast, by Application 2020 & 2033
- Table 3: Global Heads Up Display Industry Revenue billion Forecast, by Region 2020 & 2033
- Table 4: Global Heads Up Display Industry Revenue billion Forecast, by Type 2020 & 2033
- Table 5: Global Heads Up Display Industry Revenue billion Forecast, by Application 2020 & 2033
- Table 6: Global Heads Up Display Industry Revenue billion Forecast, by Country 2020 & 2033
- Table 7: United States Heads Up Display Industry Revenue (billion) Forecast, by Application 2020 & 2033
- Table 8: Canada Heads Up Display Industry Revenue (billion) Forecast, by Application 2020 & 2033
- Table 9: Global Heads Up Display Industry Revenue billion Forecast, by Type 2020 & 2033
- Table 10: Global Heads Up Display Industry Revenue billion Forecast, by Application 2020 & 2033
- Table 11: Global Heads Up Display Industry Revenue billion Forecast, by Country 2020 & 2033
- Table 12: United Kingdom Heads Up Display Industry Revenue (billion) Forecast, by Application 2020 & 2033
- Table 13: Germany Heads Up Display Industry Revenue (billion) Forecast, by Application 2020 & 2033
- Table 14: France Heads Up Display Industry Revenue (billion) Forecast, by Application 2020 & 2033
- Table 15: Rest of Europe Heads Up Display Industry Revenue (billion) Forecast, by Application 2020 & 2033
- Table 16: Global Heads Up Display Industry Revenue billion Forecast, by Type 2020 & 2033
- Table 17: Global Heads Up Display Industry Revenue billion Forecast, by Application 2020 & 2033
- Table 18: Global Heads Up Display Industry Revenue billion Forecast, by Country 2020 & 2033
- Table 19: China Heads Up Display Industry Revenue (billion) Forecast, by Application 2020 & 2033
- Table 20: Japan Heads Up Display Industry Revenue (billion) Forecast, by Application 2020 & 2033
- Table 21: South Korea Heads Up Display Industry Revenue (billion) Forecast, by Application 2020 & 2033
- Table 22: Australia Heads Up Display Industry Revenue (billion) Forecast, by Application 2020 & 2033
- Table 23: Rest of Asia Pacific Heads Up Display Industry Revenue (billion) Forecast, by Application 2020 & 2033
- Table 24: Global Heads Up Display Industry Revenue billion Forecast, by Type 2020 & 2033
- Table 25: Global Heads Up Display Industry Revenue billion Forecast, by Application 2020 & 2033
- Table 26: Global Heads Up Display Industry Revenue billion Forecast, by Country 2020 & 2033
Frequently Asked Questions
1. What is the projected Compound Annual Growth Rate (CAGR) of the Heads Up Display Industry?
The projected CAGR is approximately 14%.
2. Which companies are prominent players in the Heads Up Display Industry?
Key companies in the market include Collins Aerospace (Rockwell Collins Inc ), Denso Corporation, Visteon Corporation, Garmin Ltd, Thales Group, BAE Systems PLC, Nippon Seiki Co Ltd, Elbit Systems, Continental AG, HUDWAY LLC, Panasonic Automotive Systems (Panasonic Corporation), Saab AB, Pioneer Corporation.
3. What are the main segments of the Heads Up Display Industry?
The market segments include Type, Application.
4. Can you provide details about the market size?
The market size is estimated to be USD 6.38 billion as of 2022.
5. What are some drivers contributing to market growth?
Technological Advancements of HUD; Growing Awareness About Passenger and Vehicle Safety.
6. What are the notable trends driving market growth?
Growing Adoption of HUD in Automotive Industry Driving the Market's Growth.
7. Are there any restraints impacting market growth?
Lack of International Accepted Standards.
8. Can you provide examples of recent developments in the market?
January 2022 - CY Vision announced automotive 3D Augmented Reality Head-Up Displays (3D AR-HUD). It provides the widest field of view in augmented displays on the market today for all weather conditions and all distances.
9. What pricing options are available for accessing the report?
Pricing options include single-user, multi-user, and enterprise licenses priced at USD 4750, USD 5250, and USD 8750 respectively.
10. Is the market size provided in terms of value or volume?
The market size is provided in terms of value, measured in billion.
11. Are there any specific market keywords associated with the report?
Yes, the market keyword associated with the report is "Heads Up Display Industry," which aids in identifying and referencing the specific market segment covered.
12. How do I determine which pricing option suits my needs best?
The pricing options vary based on user requirements and access needs. Individual users may opt for single-user licenses, while businesses requiring broader access may choose multi-user or enterprise licenses for cost-effective access to the report.
13. Are there any additional resources or data provided in the Heads Up Display Industry report?
While the report offers comprehensive insights, it's advisable to review the specific contents or supplementary materials provided to ascertain if additional resources or data are available.
14. How can I stay updated on further developments or reports in the Heads Up Display Industry?
To stay informed about further developments, trends, and reports in the Heads Up Display Industry, consider subscribing to industry newsletters, following relevant companies and organizations, or regularly checking reputable industry news sources and publications.
Methodology
Step 1 - Identification of Relevant Samples Size from Population Database
Step 2 - Approaches for Defining Global Market Size (Value, Volume* & Price*)
Note*: In applicable scenarios
Step 3 - Data Sources
Primary Research
- Web Analytics
- Survey Reports
- Research Institute
- Latest Research Reports
- Opinion Leaders
Secondary Research
- Annual Reports
- White Paper
- Latest Press Release
- Industry Association
- Paid Database
- Investor Presentations
Step 4 - Data Triangulation
Involves using different sources of information in order to increase the validity of a study
These sources are likely to be stakeholders in a program - participants, other researchers, program staff, other community members, and so on.
Then we put all data in single framework & apply various statistical tools to find out the dynamic on the market.
During the analysis stage, feedback from the stakeholder groups would be compared to determine areas of agreement as well as areas of divergence